Convergence in Measure and in Category

• Autorzy: Władysław Wilczyński
• Języki publikacji: EN

Abstrakty

EN

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]. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Convergence

PL

Matematyka; Funkcje matematyczne; Konwergencja

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (1)
• Strony: 164--168

Twórcy

autor

Władysław Wilczyński

• University of Lodz, Poland

Bibliografia

• R.M. Dudley, Real Analysis and Probability, Cambridge Studies in Advanced Mathematics, 74, Cambridge University Press, Cambridge, 2002.
• E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York-Berlin, 1969.
• W. Orlicz, On a class of asymptotically divergent sequences of functions, Studia Math. 12 (1951), 286-307; Collected papers, part I, 630-651, Polish Scientific Publishers, Warszawa, 1988.
• J.C. Oxtoby, Measure and Category, second edition, Springer-Verlag, New York-Berlin, 1980.
• E. Wagner, Sequences of measurable functions, Fund. Math. 112 (1981), 89-102.

Identyfikatory

DOI

10.2478/amsil-2020-0001