Measure, Integration & Real Analysis · Problem 12.13

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · distribution-function-inverse

Problem

Suppose

H: \mathbf{R} \to (0, 1)

is a continuous one-to-one function satisfying conditions (a) through (d) of 12.29. Show that the function

X: (0,1) \to \mathbf{R}

produced in the proof of 12.29 is the inverse function of

H