Results 71 to 76 of about 107 (76)

The Theorems of Lusin and Egoroff

1971
A real-valued function f on R is called measurable if f−1(U) is measurable for every open set U in R. f is said to have the property of Baire if f −1 (U) has the property of Baire for every open set U in R. In either definition, U may be restricted to some base, or allowed to run over all Borel sets.
openaire   +1 more source

Lebesgue's theorem and Egoroff's theorem for complex uncertain sequences

In this paper, within framework uncertain theory, we investigate Lebesgue’s theorem, Egoroff’s theorem and Riesz’s theorem for complex uncertain sequences. © 2024 Elsevier B.V., All rights reserved.
Kişi, Ömer, Gürdal, Mehmet, Kişi, Ömer, Kişi, Ömer   +3 more
openaire   +3 more sources

Some remarks on Egoroff's theorem

2015
The author defines the uniform convergence of sequences of functions with respect to so-called small systems. The notion of small systems was introduced by \textit{T. Neubrunn} and \textit{B. Riečan} in their book [Measure and integral (Slovak) (Bratislava 1981; Zbl 0485.28001)].
openaire   +2 more sources

A further investigation for Egoroff's theorem with respect to monotone set functions.

Kybernetika, 2003
Summary: In this paper we investigate Egoroff's theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff's theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff's theorem for non-additive measure is formulated in full generality.
openaire   +2 more sources

A Counter-Example Concerning Egoroff's Theorem

Journal of the London Mathematical Society, 1959
openaire   +2 more sources

Set-valued Lusin type theorem for null–null-additive set multifunctions

Fuzzy Sets and Systems, 2012
Alina Gavrilut
exaly