Generalization of a real-analysis result to a class of topological vector spaces

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New Zealand Journal of Mathematics

Vol. 50, (2020), Pages 21-27


Leonard T. Huang

Department of Mathematics & Statistics

University of Nevada, Reno

1664 North Virginia Street

Reno

Nevada 89557

United States of America

mailto:LeonardHuang@unr.edu






Abstract In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.

Keywords Topological vector spaces, locally convex topological vector spaces, p-homogeneous seminorms, random variables, convergence in probability.

Classification (MSC2000) 28A20, 46A16, 60A10.

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