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On almost sure convergence in a finitely additive setting

  • Robert Chen
Article

Abstract

In their book “How To Gable If You Must”, Dubins and Savage introduced finitely additive stochastic processes in discrete time and they obtained some results about finitely additive probability measures on infinite product spaces. In the paper, “Some Finitely Additive Probability”, Purves and Sudderth showed how to extend these finitely additive probability measures and it thus became possible to consider many of the classical strong convergence theorems. In this paper, we extend many of the classical strong convergence theorems to a finitely additive setting. Since all proofs in this paper are valid for a countably additive setting if we consider the problem on a coordinate representation process, the results in this paper are generalizations of the classical results on such a process. Some examples are also provided for contrasting a finitely additive setting with a countably additive setting.

Keywords

Stochastic Process Probability Measure Probability Theory Discrete Time Mathematical Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Robert Chen
    • 1
  1. 1.Department of MathematicsUniversity of MiamiCoral GablesUSA

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