Show that an unsigned function f: 𝐑^d →[0,+∞] is a simple function if and only if it is measurab

Question

Show that an unsigned function $f: \mathbf{R}^d \rightarrow[0,+\infty]$ is a simple function if and only if it is measurable and takes on at most finitely many values.

   Show that an unsigned function $f: \mathbf{R}^d \rightarrow[0,+\infty]$ is a simple function if and only if it is measurable and takes on at most finitely many values.

An Introduction To Measure Theory (January 2011 Draft)

Terence Tao 1st Edition

Chapter 1, Problem 5

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Show that an unsigned function $f: \mathbf{R}^d \rightarrow[0,+\infty]$ is a simple function if and only if it is measurable and takes on at most finitely many values.