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Results tagged with real-analysis
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user 99418
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
6
votes
Accepted
Is the Legendre transform as an operator Lipschitz?
This is basically true for sup norm by Fenchel's inequality. Indeed, for all $y$,
$$
f^*(y) = \sup_x\left( \langle x,y\rangle - f(x) \right) \leq \sup_x\left( g(x)+g^*(y) - f(x) \right) \leq \|f-g\|_ …
- 716
3
votes
Accepted
Transforming two smooth densities to the same density
This is impossible if $f$ is injective, without further assumptions such as bijective, differentiable, etc. Let $Q_1,Q_2$ be probability measures on a measurable space $(\Omega, \mathcal{F})$, and as …
- 716