Introduction to Math Analysis Lecture 10 Minkowskis And Other Inequalities

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=wR18ADK_K8U

We establish triangle inequality for the p-norms by proving Young's, , Hölder's, Minkowski's, and various other inequalities.","styleRuns":[{"startIndex":0,"length":125,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":125,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"COABELsvGAIiEwiujeXX38qLAxXxc3oFHTsbHtg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC3dSMThBREtfSzhVGAYyJSIRIgt3UjE4QURLX0s4VTAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"COABELsvGAIiEwiujeXX38qLAxXxc3oFHTsbHtg=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CN8BELovIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"8whuSgr0RE8","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/8whuSgr0RE8/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLAj9OycrQWP9wUv0t046Nb2di5GDQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/8whuSgr0RE8/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCrX4LIp4xJg3UmrE28V20_FAXc3w","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Introduction to Math Analysis (Lecture 11): Limits In Abstract Metric Spaces by Arkady Etkin 710 views 6 years ago 1 hour, 10 minutes"}},"simpleText":"Introduction to Math Analysis (Lecture 11): Limits In Abstract Metric Spaces"},"longBylineText":{"runs":[{"text":"Arkady Etkin","navigationEndpoint":{"clickTrackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@arkadyetkin3735","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC8gsgnJ66Cyx1HVtSKOjYTw","canonicalBaseUrl":"/@arkadyetkin3735"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"710 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"1 hour, 10 minutes, 53 seconds"}},"simpleText":"1:10:53"},"navigationEndpoint":{"clickTrackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWRIxdf8lYOA347BAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=8whuSgr0RE8","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"8whuSgr0RE8","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=f3086e4a0af4444f ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1453750 mt=1739796541 oweuc= pxtags=Cg4KAnR4Egg1MTM4OTU4Mw rxtags=Cg4KAnR4Egg1MTM4OTU4Mg%2CCg4KAnR4Egg1MTM4OTU4Mw"}}}}},"shortBylineText":{"runs":[{"text":"Arkady Etkin","navigationEndpoint":{"clickTrackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@arkadyetkin3735","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC8gsgnJ66Cyx1HVtSKOjYTw","canonicalBaseUrl":"/@arkadyetkin3735"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_n7talTpG41xGIGRTrh60vkLTT12AiicKbWjkGv-40dGQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHthAz4jR16DJm4TzAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"710 views"}},"simpleText":"710 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CN0BEP6YBBgFIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CN0BEP6YBBgFIhMIro3l19_KiwMV8XN6BR07Gx7Y","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"8whuSgr0RE8","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CN0BEP6YBBgFIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["8whuSgr0RE8"],"params":"CAQ%3D"}},"videoIds":["8whuSgr0RE8"]}},{"clickTrackingParams":"CN0BEP6YBBgFIhMIro3l19_KiwMV8XN6BR07Gx7Y","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CN4BELlqIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},"popupType":"TOAST"}}]}},"trackingParams":"CN0BEP6YBBgFIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNwBENGqBRgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","offlineVideoEndpoint":{"videoId":"8whuSgr0RE8","onAddCommand":{"clickTrackingParams":"CNwBENGqBRgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","getDownloadActionCommand":{"videoId":"8whuSgr0RE8","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNwBENGqBRgGIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs4d2h1U2dyMFJFOA%3D%3D","commands":[{"clickTrackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNsBEI5iIhMIro3l19_KiwMV8XN6BR07Gx7Y","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtg=","hasSeparator":true}}],"trackingParams":"CNgBEKQwGAAiEwiujeXX38qLAxXxc3oFHTsbHtg=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"1 hour, 10 minutes, 53 seconds"}},"simpleText":"1:10:53"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNoBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"8whuSgr0RE8","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CNoBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"8whuSgr0RE8"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNoBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNkBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNkBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"8whuSgr0RE8","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNkBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["8whuSgr0RE8"],"params":"CAQ%3D"}},"videoIds":["8whuSgr0RE8"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNkBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Introduction to Math Analysis (Lecture 11): Limits In Abstract Metric Spaces - 1 hour, 10 minutes - Go to channel - Arkady Etkin - 710 views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"vQm2wiuDHh0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/vQm2wiuDHh0/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDbCSa5iVVczditRxbKcSf8TxQSbA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/vQm2wiuDHh0/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLA2VFDGnR3zvFPu7AcAzWtjwd0ISg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"minkowski inequality proof by E-Academy 16,141 views 6 years ago 9 minutes, 49 seconds"}},"simpleText":"minkowski inequality proof"},"longBylineText":{"runs":[{"text":"E-Academy","navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@E-Academy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCCLENXH3qTlHc-M24zHgr2Q","canonicalBaseUrl":"/@E-Academy"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"16,141 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWRIxdf8lYOA347BAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=vQm2wiuDHh0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"vQm2wiuDHh0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=bd09b6c22b831e1d ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1676250 mt=1739796541 oweuc= pxtags=Cg4KAnR4Egg1MTM4OTU4Mw rxtags=Cg4KAnR4Egg1MTM4OTU4Mg%2CCg4KAnR4Egg1MTM4OTU4Mw"}}}}},"shortBylineText":{"runs":[{"text":"E-Academy","navigationEndpoint":{"clickTrackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@E-Academy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCCLENXH3qTlHc-M24zHgr2Q","canonicalBaseUrl":"/@E-Academy"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_mDSCRC02BRh2QveHyEq8p2ig59_qMRKIAhHYhzfXNNDw=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHthAnbyM3KLY7YS9AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"16K views"}},"simpleText":"16K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNYBEP6YBBgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNYBEP6YBBgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"vQm2wiuDHh0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNYBEP6YBBgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["vQm2wiuDHh0"],"params":"CAQ%3D"}},"videoIds":["vQm2wiuDHh0"]}},{"clickTrackingParams":"CNYBEP6YBBgGIhMIro3l19_KiwMV8XN6BR07Gx7Y","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNcBELlqIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},"popupType":"TOAST"}}]}},"trackingParams":"CNYBEP6YBBgGIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNUBENGqBRgHIhMIro3l19_KiwMV8XN6BR07Gx7Y","offlineVideoEndpoint":{"videoId":"vQm2wiuDHh0","onAddCommand":{"clickTrackingParams":"CNUBENGqBRgHIhMIro3l19_KiwMV8XN6BR07Gx7Y","getDownloadActionCommand":{"videoId":"vQm2wiuDHh0","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNUBENGqBRgHIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt2UW0yd2l1REhoMA%3D%3D","commands":[{"clickTrackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNQBEI5iIhMIro3l19_KiwMV8XN6BR07Gx7Y","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtg=","hasSeparator":true}}],"trackingParams":"CNEBEKQwGAEiEwiujeXX38qLAxXxc3oFHTsbHtg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNMBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"vQm2wiuDHh0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CNMBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"vQm2wiuDHh0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNMBEPnnAxgBIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNIBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNIBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"vQm2wiuDHh0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNIBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["vQm2wiuDHh0"],"params":"CAQ%3D"}},"videoIds":["vQm2wiuDHh0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNIBEMfsBBgCIhMIro3l19_KiwMV8XN6BR07Gx7Y"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"minkowski inequality proof - 9 minutes, 49 seconds - Go to channel - E-Academy - 16K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/vQm2wiuDHh0/mqdefault_6s.webp?du=3000 sqp=CNS8zL0G rs=AOn4CLBvTzDDNUUFO_LhxJSG3aS4yc58AQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/zLCbytDWMGs/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLBH_4iv2QIvME_Q1xffwNiEPW5Bcw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/zLCbytDWMGs/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLD4XlPJR2GcQHeKvn02PmPF6gEjjA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"39 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"functional analysis"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"E-Academy

#############################