hw4 - Mathematics 105, Spring 2004 - Problem Set IV For the...

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Mathematics 105, Spring 2004 — Problem Set IV For the remainder of the semester we will follow the text A Concise Introduction to the Theory of Integration (second edition) by Stroock. Problem, chapter, section, and page numbers refer to that text unless otherwise indicated. For Friday February 27 : You should have already read § 2.0 and begun reading § 2.1. Finish studying § 2.1. Also read Lemma 1.1.1 and its proof; the whole theory of Lebesgue integration relies on this (semitrivial) lemma. Solve problems 2.1.18,19 of Stroock, and the following problems: IV.A Let { I n } be any finite set of open intervals that covers [0 , 1] Q . Show that n | I n | ≥ 1. Explain why this does not prove that | [0 , 1] Q | e 1. IV.B Show that for any Lebesgue measurable sets A, B R n , | A B | + | A B | = | A | + | B | . IV.C Let A R n and suppose that | A | e = 0. Prove that for any set B R n , | A B | e = | B | e . IV.D
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This note was uploaded on 05/07/2008 for the course MATH 105 taught by Professor Michaelchrist during the Spring '04 term at Berkeley.

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