• JUN KAWABE Department of Mathematics, Faculty of Engineering, Shinshu University, Wakasato, Nagano 380, Japan.




Transition probability, compound probability measure, upper semicontinuous, set-valued mapping, uniform tighness, Gaussian, nuclear space


The aim of this paper is to give a notion of uniform tightness for transition probabilities on topological spaces, which assures the uniform tightness of compound probability measures. Then the upper semicontinuity of set-valued mappings are used in essence. As an important example, the uniform tightness for Gaussian transition probabilities on the strong dual of a nuclear real Frechet space is studied. It is also shown that some of our results contain well-known results concerning the uniform tightness and the weak convergence of probability measures.


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How to Cite

KAWABE, J. (1995). UNIFORM TIGHTNESS FOR TRANSITION PROBABILITIES. Tamkang Journal of Mathematics, 26(4), 283–298. https://doi.org/10.5556/j.tkjm.26.1995.4408