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.References
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Additional Information
- Elżbieta Wagner-Bojakowska
- Affiliation: Faculty of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
- Email: wagner@krysia.uni.lodz.pl
- Władysław Wilczyński
- Affiliation: Faculty of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
- Email: wwil@krysia.uni.lodz.pl
- Received by editor(s): November 15, 1995
- Received by editor(s) in revised form: March 10, 1996
- Published electronically: October 12, 1999
- Communicated by: Franklin D. Tall
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 413-418
- MSC (1991): Primary 28A20, 54A20; Secondary 26A03
- DOI: https://doi.org/10.1090/S0002-9939-99-05578-1
- MathSciNet review: 1707533