journal6 ›› 2008, Vol. 29 ›› Issue (2): 25-26.

• Mathematics • Previous Articles     Next Articles

On Spaces of All Probabilities on Polish Spaces


  1. (Hunan Financial and Economic College,Changsha 410205,China)
  • Online:2008-03-25 Published:2012-05-25

Abstract: Assume S is a Polish space and M1(s) the space of all probabilities on it.Endow M1(s) with the weak topology.Let {Xn}n≥1 be a sequence of random variables M1(s)-valued and {μn}n≥1 its first moment measure sequence.Then {Xn}n≥1 is exponentially tight on M1(s) provided so is {μn}n≥1 on S.Moreover,when S is locally compact,the weak topology on M1(s) can be induced by the following metric:d(μ,μ-)=supf∈F|μ(f)-μ(f)|μ,μ-∈M1(S),where,F is the set of bounded continuous functions on S with α-Hlder norm is uniformly bounded by a C>0,and α∈(0,1].

Key words: exponentially tight, first moment measure, weak topology, Hlder continuous

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