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Results tagged with real-analysis
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user 58975
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
5
votes
1
answer
324
views
Convergence in energy of bounded (semi)subharmonic functions
Consider a sequence $(f_n)$ of functions in the flat torus $T^d$ converging Lebesgue-a.e. to a limit function $f$.
Assume that:
1) $|f_n|(x)\leq 1$ for every $n,x$
2) $\Delta f_n\geq -1$ in the sen …
- 660
3
votes
Convergence in energy of bounded (semi)subharmonic functions
I'm reporting an example, presented to me by Bozhidar Velichkov, showing that the answer to my question is no.
The example is based on a construction by Cioranescu-Murat given in their paper "Un ter …
- 660
1
vote
Continuity and sequential continuity of a linear functional
Another way of seeing that the answer is affirmative is to realize that the topology on $E$ is the inductive limit of the topologies on $C(K,R^m)$ (see e.g. https://en.wikipedia.org/wiki/Final_topolog …
- 660
7
votes
Accepted
About the metrizability of the space of Probability measures $\mathcal{P}(S)$
I'm not really sure what Villani wrote in his monograph, but it is true that one needs to prove that the weak topology is induced by a distance, as a priori it could be another topology with the same …
- 660