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Results tagged with real-analysis
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user 123897
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
5
votes
Functions that map open balls to open balls of different radius?
For $n\ge 2$ every balloon map is a composition of a scaling, a translation and a rotation/reflection.
The following proof is incomplete as it relies on the fact that the boundary of a ball is mappe …
- 576
2
votes
Accepted
Kantorovich duality with pseudometrics
Yes the Kantorovich Duality holds for continuous cost functions by following the proof in Villani's book without any change. The proof for general cost functions needs compactness of the set of coupli …
- 576
10
votes
Derivative of distance function to a closed, rectifiable set
The distance $f: x \mapsto \mathsf{dist}(x,\Gamma)$ to a closed set $\Gamma$ in $\mathbb{R}^n$ is differentiable in $x \notin \Gamma$ iff the nearest point projection is unique; denote this by $x_\Gam …
- 576