21-356 Lecture 29

Hence 0 sup meas p p pluri rectangle e 5 p

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Unformatted text preview: \ E % ) P2 \ P1 . Hence, 0 % sup {meas P : P pluri-rectangle, # E 5 P } ' ( % % inf {meas P : P pluri-rectangle, # E ) P } % meas P2 \ P1 % (, which, by letting ( * 0+ , implies that 0 = sup {meas P : P pluri-rectangle, # E 5 P } = inf {meas P : P pluri-rectangle, # E ) P } = 0. It follows by the previous theorem that # E is Peano—Jordan measurable with measure zero. Step 2: Assume that # E ) RN is Peano—Jordan measurable with measure zero. Since E is bounded, so is E and so there exists a rectangle R containing...
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This document was uploaded on 03/31/2014.

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