Cauchy condition for the convergence in category

Wagner-Bojakowska, Elżbieta; Wilczyński, Władysław

doi:10.1090/S0002-9939-99-05578-1

Cauchy condition for the convergence in category
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by Elżbieta Wagner-Bojakowska and Władysław Wilczyński PDF

Proc. Amer. Math. Soc. 128 (2000), 413-418 Request permission

Abstract:

It is well known that the sequence $\{f_n\}_{n\in N}$ of real measurable functions converges in measure to some measurable function $f$ if and only if $\{f_n\}_{n\in N}$ is fundamental in measure. In this note we introduce the notion of sequence fundamental in category in this manner such that the sequence $\{f_n\}_{n\in N}$ of real functions having the Baire property converges in category to some function $f$ having the Baire property if and only if $\{f_n\}_{n\in N}$ is fundamental in category.

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