Convergence in Measure and in Category
Abstract
W. Orlicz in 1951 has observed that if {fn(·, y)}n∈N converges in measure to f(·, y) for each y ∈ [0, 1], then {fn}n∈N converges in measure to f on [0, 1] × [0, 1]. The situation is different for the convergence in category even if we assume the convergence in category of sequences {fn(·, y)}n∈N for each y ∈ [0, 1] and {fn(x, ·)}n∈N for each x ∈ [0, 1].
Language: English
Page range: 164 - 168
Submitted on: Oct 2, 2019
Accepted on: Feb 29, 2020
Published on: May 8, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2020 Władysław Wilczyński, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.