Measure, Integration & Real Analysis · Problem 4A.12

Product Measures — Sheldon Axler

Mathematics — Measure Theory · hardy-littlewood-maximal-infinite-set-measure-zero

Problem

Show that

|\{b \in \mathbf{R} : h^*(b) = \infty\}| = 0

for every

h \in \mathcal{L}^1(\mathbf{R})