11 Prove that if A C R and |A| > 0, then there exists a subset of A that is notLebesgue measurable.12 Suppose b < c and A C (b,c). Prove that A is Lebesgue measurable if andonly if |A| + |(b,c) \ A| = c – b.13 Suppose AC R. Prove that A is Lebesgue measurable if and only if|(-n,n) N A| + |(-n,n) \ A| = 2n

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 32EQ

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11 Prove that if A CR and |A| > 0, then there exists a subset of A that is not Lebesgue measurable.