Suppose[FN1] 2 is Lebesgue measure on R and f: R → R is a Borel measurable function such that belongs to L¹(R). Define g: R → R by g(x) = st*fdx. Prove that g is uniformly continuous on R.
Suppose[FN1] 2 is Lebesgue measure on R and f: R → R is a Borel measurable function such that belongs to L¹(R). Define g: R → R by g(x) = st*fdx. Prove that g is uniformly continuous on R.
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[FN1] is Lebesgue measure on R and f: R → R is a Borel measurable function
such that belongs to L¹(R). Define g: R → R by
fdλ.
g(²) J-00
=
Prove that g is uniformly continuous on R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F503bef97-0a89-4e34-8b8c-b76f4dabcdee%2F3abd26ce-c671-49b8-9534-ed0b60afd7b6%2Fqbzuyl_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose[FN1] is Lebesgue measure on R and f: R → R is a Borel measurable function
such that belongs to L¹(R). Define g: R → R by
fdλ.
g(²) J-00
=
Prove that g is uniformly continuous on R.
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