Measure, Integration & Real Analysis · Problem 4A.9

Product Measures — Sheldon Axler

Mathematics — Measure Theory · hardy-littlewood-maximal-open-set

Problem

Suppose

h: \mathbf{R} \to \mathbf{R}

is Lebesgue measurable. Prove that

\{b \in \mathbf{R} : h^*(b) > c\}

is an open subset of

\mathbf{R}

for every

c \in \mathbf{R}