4. Let f: RR be a Lebesgue measurable function. Prove that there exists a Borel measurable function g: R → R such that {r ER| f(x) = g(x)} = 0.
4. Let f: RR be a Lebesgue measurable function. Prove that there exists a Borel measurable function g: R → R such that {r ER| f(x) = g(x)} = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 12E
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![4.
Let f RR be a Lebesgue measurable function. Prove
that there exists a Borel measurable function g: R → R such that
{x ≤R f(x) = g(x)}| = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32810b9b-7ce5-4d0b-a2ce-fedb80cee835%2F10a50696-59a9-41c2-b249-a69c65cdaeaf%2Fdv5u8os_processed.png&w=3840&q=75)
Transcribed Image Text:4.
Let f RR be a Lebesgue measurable function. Prove
that there exists a Borel measurable function g: R → R such that
{x ≤R f(x) = g(x)}| = 0.
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