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Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0. Prove that if B = {x – y : x, y E A},

Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0. Prove that if B = {x – y : x, y E A},

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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need assistance with real analysis Lesbegure measure and steinhaus theorem. Thankyou for clear explanation and your time.

Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0. Prove that if B = {x – y : x, Y E A}, {X – Y : x, y E A}, then B contains a non-empty open interval centered at the origin. This is known as the Steinhaus theorem.
Transcribed Image Text:Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0. Prove that if B = {x – y : x, Y E A}, {X – Y : x, y E A}, then B contains a non-empty open interval centered at the origin. This is known as the Steinhaus theorem.
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