We prove that a closed, geodesically convex subset C of $P_2^r(R^d)$ is closed with respect to weak convergence in $P_2^r(R^d)$. This means that if $(mu_n)subset C$ is such that $mu_n omu$ in duality with continuous bounded functions and have uniformly bounded second moments, then $mu$ is in C as well
Weak closure of geodesically convex subsets of Probability measures / Gigli, Nicola. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - (2009).
Weak closure of geodesically convex subsets of Probability measures
Gigli, Nicola
2009-01-01
Abstract
We prove that a closed, geodesically convex subset C of $P_2^r(R^d)$ is closed with respect to weak convergence in $P_2^r(R^d)$. This means that if $(mu_n)subset C$ is such that $mu_n omu$ in duality with continuous bounded functions and have uniformly bounded second moments, then $mu$ is in C as wellFile in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
weakclosureconvexsets.pdf
non disponibili
Licenza:
Non specificato
Dimensione
189.95 kB
Formato
Adobe PDF
|
189.95 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
