A Characterization of Probabilities with Full Support and the Laplace Method

  • Simone Cerreia-Vioglio
  • Fabio MaccheroniEmail author
  • Massimo Marinacci


We show that a probability measure on a metric space 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 Borel probability measures. We illustrate the result through a general version of Laplace’s method, which in turn leads to general stochastic convergence to global maxima.


Absolute continuity Support of a measure Laplace method 

Mathematics Subject Classification

46N30 46N10 60B05 



We thank Giacomo Cattelan, Ludovica Ciasullo, and Isabella Morgan Wolfskeil for excellent research assistance. Simone Cerreia-Vioglio, and Fabio Maccheroni and Massimo Marinacci gratefully acknowledge the financial support of ERC (Grants SDDM-TEA and INDIMACRO, respectively).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Simone Cerreia-Vioglio
    • 1
  • Fabio Maccheroni
    • 1
    Email author
  • Massimo Marinacci
    • 1
  1. 1.IGIERBocconi UniversityMilanItaly

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