We show that a probability measure on a metric space X has full support if and only if the set of all probability measures that are absolutely continuous with respect to it is dense in the set of all probability measures on X. We illustrate the result through a general version of Laplace method, which in turn leads to a general stochastic convergence result to global maxima.

A characterization of probabilities with full support and the Laplace method

Cerreia-Vioglio, Simone;Maccheroni, Fabio
;
Marinacci, Massimo
2019

Abstract

We show that a probability measure on a metric space X has full support if and only if the set of all probability measures that are absolutely continuous with respect to it is dense in the set of all probability measures on X. We illustrate the result through a general version of Laplace method, which in turn leads to a general stochastic convergence result to global maxima.
2019
Cerreia-Vioglio, Simone; Maccheroni, Fabio; Marinacci, Massimo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/4023138
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