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Results tagged with measurable-functions
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user 498220
2
votes
2
answers
275
views
Preimage of null sets under a monotone increasing function
Let $I\subseteq \mathbb{R}$ be a closed bounded interval and $f:I \to I$ a monotonic increasing function and $S$ the countable set of points $s$ such that $|f^{-1}(s)| > 1$. Is the following conjectur …
- 113
2
votes
Accepted
Preimage of null sets under a monotone increasing function
My colleague and I came up with a proof for the following related Theorem:
Let $I \subseteq \mathbb{R}$ be an interval, $f:I\to I$ an absolutely continuous monotone increasing function. Define $I_{f'> …
- 113