<abstract xmlns="http://www.w3.org/1999/xhtml">W. Orlicz in 1951 has observed that if {<italic>fn</italic>(<italic>·, y</italic>)}<italic>n</italic>∈<italic>N</italic> converges in measure to <italic>f</italic>(<italic>·, y</italic>) for each <italic>y</italic> ∈ [0, 1], then {<italic>fn</italic>}<italic>n</italic>∈<italic>N</italic> converges in measure to <italic>f</italic> on [0, 1] <italic>×</italic> [0, 1]. The situation is different for the convergence in category even if we assume the convergence in category of sequences {<italic>fn</italic>(<italic>·, y</italic>)}<italic>n</italic>∈<italic>N</italic> for each <italic>y</italic> ∈ [0, 1] and <italic>{fn</italic>(<italic>x, ·</italic>)<italic>}n</italic>∈<italic>N</italic> for each <italic>x</italic> ∈ [0, 1].</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].

Convergence in Measure and in Category

Faculty of Mathematics and Computer Science

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Convergence in Measure and in Category"}

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] ×...

Convergence in Measure and in Category

Published Online: May 08, 2020

Page range: 164 - 168

Received: Oct 02, 2019

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0001

Keywords
convergence in measure, convergence in category

© 2020 Władysław Wilczyński, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Convergence in Measure and in Category

Published Online: May 08, 2020

Page range: 164 - 168

Received: Oct 02, 2019

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0001

Keywordsconvergence in measure, convergence in category

© 2020 Władysław Wilczyński, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
convergence in measure, convergence in category