Measure, Integration & Real Analysis · Problem 4A.13

Product Measures — Sheldon Axler

Mathematics — Measure Theory · hardy-littlewood-maximal-infinite-on-rationals

Problem

Show that there exists

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

such that

h^*(b) = \infty

for every

b \in \mathbf{Q}