All Questions
Tagged with descriptive-set-theory measurable-functions
3 questions
3
votes
1
answer
155
views
Can there be an upper bound on the Borel rank of the preimages of Borel sets under a surjective Borel map?
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 ...
3
votes
0
answers
76
views
Can we generalize the Kuratowski Extension Theorem to Souslin spaces?
The Kuratowski Extension Theorem says: Let $(X,\mathcal{A})$ be a measurable space, $Y$ be a polish space, $A\subseteq X$, and $f:A\to Y$ be a measurable map. Then there is a measurable function $F:X\...
- 627
1
vote
1
answer
208
views
Function $g:\mathbb{R}\to \mathbb{R}^n$ such that $g(\sum_{i=1}^nx_i)=(x_1,\dotsc,x_n)$ a.e
Is there a measurable function $g:\mathbb{R}\to \mathbb{R}^n$ such that $g(\sum_{i=1}^nx_i)=(x_1,\dotsc,x_n)$ a.e.?
Due to the papers [1], [2], and [3] I'm obtaining a result that I think it's false. ...
- 627