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#### TheBigBadBen

##### Active member

- May 12, 2013

- 84

Suppose that \(\displaystyle f:\mathbb{R}\rightarrow\mathbb{R}\) is a measurable function and that \(\displaystyle g:\mathbb{R}\rightarrow\mathbb{R}\) is a Borel (i.e. Borel measurable) function. Show that \(\displaystyle f\circ g\) is measurable.

If we only assume that g is measurable, is it still true that the composition \(\displaystyle f\circ g\) is measurable?