Measure, Integration & Real Analysis · Problem 4B.5

Product Measures — Sheldon Axler

Mathematics — Measure Theory · lebesgue-differentiation-maximal-inequality

Problem

Suppose

f: \mathbf{R} \to \mathbf{R}

is a Lebesgue measurable function. Prove that

|f(b)| \leq f^*(b)

for almost every

b \in \mathbf{R}