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Can we conclude that an analytic subset $A$ of a Polish space $X$ is also Polish? Let $\mathcal{M}(R^d)$ denotes the family of Borel probability measures on $R^d$ equipped with the Lévy-Prokhorov ...

I found this problem I have tried but it has been a bit complicated for me, Let $f:\mathbb{R}\to\mathbb{R}$ a bounded function. For each $\epsilon>0$, let $f_\epsilon (x)=\inf\{f(y):|y-x|<\...

Let $X$ and $Y$ be standard Borel spaces, $Y$ uncountable, and $f : X \to Y$ a surjective Borel map. Is it possible that there is a countable ordinal $\alpha$ such that for each Borel set $B \subseteq ...