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Exercise 4.2 Let m be Lebesgue measure and A a Lebesgue mea- surable subset of R with m(A) < ∞. Let e > 0. Show there exist G open and F closed such that F C ACG and m(G – F) < ɛ.

Exercise 4.2 Let m be Lebesgue measure and A a Lebesgue mea- surable subset of R with m(A) < ∞. Let e > 0. Show there exist G open and F closed such that F C ACG and m(G – F) < ɛ.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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I need assistance with Lebegue measure question in Real analysis, Thankyou in advance for explaining.

Exercise 4.2 Let \( m \) be Lebesgue measure and \( A \) a Lebesgue measurable subset of \(\mathbb{R}\) with \( m(A) < \infty \). Let \( \varepsilon > 0 \). Show there exist \( G \) open and \( F \) closed such that \( F \subset A \subset G \) and \( m(G - F) < \varepsilon \).
Transcribed Image Text:Exercise 4.2 Let \( m \) be Lebesgue measure and \( A \) a Lebesgue measurable subset of \(\mathbb{R}\) with \( m(A) < \infty \). Let \( \varepsilon > 0 \). Show there exist \( G \) open and \( F \) closed such that \( F \subset A \subset G \) and \( m(G - F) < \varepsilon \).
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