Suppose A is a Borel measurable subset of [0, 1], m is Lebesgue measure, and & € (0,1). Prove that there exists a continuous function f: [0, 1]→ R such that 0 ≤f≤ 1 and m({x: f(x) #XA (x)}) < E.
Suppose A is a Borel measurable subset of [0, 1], m is Lebesgue measure, and & € (0,1). Prove that there exists a continuous function f: [0, 1]→ R such that 0 ≤f≤ 1 and m({x: f(x) #XA (x)}) < E.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose A is a Borel measurable subset of [0, 1], m
is Lebesgue measure, and ɛ E (0,1). Prove that there exists a
continuous function f: [0,1] → R such that 0 <ƒ<1 and
m({x: f(x) # XA (x)}) < e.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F466c1bc3-d7a1-4ee8-8d6b-77eb6142e794%2F044b4902-9295-42c2-af5b-ae597c8644db%2F8y9i7mz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose A is a Borel measurable subset of [0, 1], m
is Lebesgue measure, and ɛ E (0,1). Prove that there exists a
continuous function f: [0,1] → R such that 0 <ƒ<1 and
m({x: f(x) # XA (x)}) < e.
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