Integral norm discretization and related problems

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mpeg4
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MPEG-4 Video (360p quality for download)   -   download
File size: 667.10 MB
Width: 640, Height: 360
Duration: 45 mins 53 secs
Frame rate: 29.97 fps, Sample rate: 44100 Hz
Average bitrate: 1.93 Mbits/sec
webm
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WebM (360p quality for download)   -   download
File size: 173.98 MB
Width: 640, Height: 360
Duration: 45 mins 54 secs
Frame rate: 29.97 fps, Sample rate: 44100 Hz
Average bitrate: 517.52 kbits/sec
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iPod Video (high quality for download)   -   download
File size: 175.22 MB
Width: 480, Height: 270
Duration: 45 mins 53 secs
Frame rate: 29.97 fps, Sample rate: 44100 Hz
Average bitrate: 521.4 kbits/sec
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File size: 84.04 MB
Duration: 45 mins 56 secs
Sample rate: 44100 Hz
Average bitrate: 249.79 kbits/sec