Measure, Integration & Real Analysis · Problem 2B.26

Measures — Sheldon Axler

Mathematics — Measure Theory · monotone-functions

Problem

Suppose

B \subseteq \mathbf{R}

and

f : B \to \mathbf{R}

is a bounded increasing function. Prove that there exists an increasing function

g : \mathbf{R} \to \mathbf{R}

such that

g(x) = f(x)

for all

x \in B