PDF-REGULARITYLEMMASFORGRAPHS3ofUandU0satisfyingforexamplejU\VijjU0\Vijfo
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jVj2t1Xi1tXji1d2ViVjjVijjVjjNotethatitfollowsdirectlyfromthede nitionoftheindexthatforanypartitionPwehave0indP1FortheproofofTheorem1wewillusethefollowingconsequenceoftheCauchySchwarzi
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