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f(x+t) - f(x) is locally integrable for all t

Source: Miklós Schweitzer 2019, Problem 8

December 27, 2019
real analysiscollege contestsMiklos Schweitzer

Problem Statement

Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a measurable function such that f(x+t)−f(x)f(x+t) - f(x) is locally integrable for every tt as a function of xx. Prove that ff is locally integrable.
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