Give an example of a measurable function and a continuous function so that ・ is non-measurable.
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Look here: https://math.stackexchange.com/questions/235718/composition-of-measurable-function-and-continuous-function?noredirect=1&lq=1 – twnly May 14 '19 at 05:16
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$f\cdot g$ or $f\circ g$? – YuiTo Cheng May 14 '19 at 05:17
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The answer depends on what you mean by measurable. You have not even specified the domain and range so there is no definite answer to this question. – Kavi Rama Murthy May 14 '19 at 05:31
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@KaviRamaMurthy different than this one $g:(X,\mathcal B(X))\to(Y,\tau_Y)$ for $g$ for sure and $f:X\to Y$ arbitrary I think – May 14 '19 at 05:36