4. Let ƒ : R → R be integrable with respect to the Lebesgue measure. Show that the function g: [0, ∞) → R defined by g(t) = sup{ [ \ƒ(x + y) — f(x)|da : \y| ≤ t} R for t> 0 is continuous at t = 0.
4. Let ƒ : R → R be integrable with respect to the Lebesgue measure. Show that the function g: [0, ∞) → R defined by g(t) = sup{ [ \ƒ(x + y) — f(x)|da : \y| ≤ t} R for t> 0 is continuous at t = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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