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

### From NZJM

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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

**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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