Results 61 to 70 of about 85 (70)

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

New Conditions for the Egoroff Theorem in Non-additive Measure Theory

2010
This paper gives a new necessary condition and a new sufficient condition for the Egoroff theorem in non-additive measure theory. The new necessary condition is condition (M), which is newly defined in this paper, and the new sufficient condition is the conjunction of null continuity and condition (M).
Masayuki Takahashi, Toshiaki Murofushi
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The Egoroff theorem for non-additive measures in Riesz spaces

Fuzzy Sets and Systems, 2006
For a \(\sigma\)-algebra \(\mathcal{F}\) on a set \(X\) and a Riesz space \(V\), an increasing mapping \(\mu: \mathcal{F} \to V\), with \( \mu(\emptyset) =0\) is called a non-additive measure. \(\mu\) is called continuous from below if \( A_{n} \downarrow A \) implies \(\mu( A_{n}) \downarrow \mu( A)\), and continuous from above if \( A_{n} \uparrow A \
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On sufficient condition for the Egoroff theorem of an ordered vector space-valued non-additive measure

Fuzzy Sets and Systems, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On sufficient conditions for the Egoroff theorem of an ordered topological vector space-valued non-additive measure

Fuzzy Sets and Systems, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
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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)].
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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.
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A Counter-Example Concerning Egoroff's Theorem

Journal of the London Mathematical Society, 1959
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Measure Riesz spaces and the Egoroff theorem

1970
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