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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cauchy condition
for the convergence in category


Authors: Elzbieta Wagner-Bojakowska and Wladyslaw Wilczynski
Journal: Proc. Amer. Math. Soc. 128 (2000), 413-418
MSC (1991): Primary 28A20, 54A20; Secondary 26A03
Published electronically: October 12, 1999
MathSciNet review: 1707533
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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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Additional Information

Elzbieta Wagner-Bojakowska
Affiliation: Faculty of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
Email: wagner@krysia.uni.lodz.pl

Wladyslaw Wilczynski
Affiliation: Faculty of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
Email: wwil@krysia.uni.lodz.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05578-1
PII: S 0002-9939(99)05578-1
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
Article copyright: © Copyright 1999 American Mathematical Society