Measure, Integration & Real Analysis · Problem 11C.10

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · convolution-uniform-continuity

Problem

Suppose

1 \leq p \leq \infty

f \in L^p(\mathbf{R})

, and

g \in L^{p'}(\mathbf{R})

. Prove that

f * g

is a uniformly continuous function on

\mathbf{R}