p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c0

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

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Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

Journal of Mathematics ◽

10.1155/2021/6655630 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Ömer Kişi

Keyword(s):

Statistical Convergence ◽

Double Sequence ◽

Finite Measure ◽

Measurable Space ◽

Double Sequences ◽

Convergence In Measure ◽

Measurable Functions ◽

Lacunary Statistical Convergence ◽

Convergence Of Sequences ◽

Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

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Spaces of measurable functions

Open Mathematics ◽

10.2478/s11533-013-0236-6 ◽

2013 ◽

Vol 11 (7) ◽

Cited By ~ 2

Author(s):

Piotr Niemiec

Keyword(s):

Hilbert Space ◽

Measure Space ◽

Finite Measure ◽

Metrizable Space ◽

Equivalence Classes ◽

Convergence In Measure ◽

Measurable Functions ◽

Almost Everywhere ◽

Finite Measure Space ◽

Completely Metrizable

AbstractFor a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.

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Distance of convergence in measure on spaces of measurable functions

Positivity ◽

10.1007/s11117-018-0621-2 ◽

2018 ◽

Vol 23 (3) ◽

pp. 507-521

Author(s):

Mehmet Unver ◽

Sevda Sagiroglu

Keyword(s):

Convergence In Measure ◽

Measurable Functions

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A note on convergence in measure and selection principles

Filomat ◽

10.2298/fil1203473d ◽

2012 ◽

Vol 26 (3) ◽

pp. 473-477

Author(s):

Dragan Djurcic ◽

Ljubisa Kocinac

Keyword(s):

Uniform Convergence ◽

Almost Everywhere Convergence ◽

Convergence In Measure ◽

Mean Convergence ◽

Measurable Functions ◽

Almost Everywhere ◽

Selection Principles ◽

Almost Uniform Convergence ◽

Special Modes

It is proved that some classes of sequences of measurable functions satisfy certain selection principles related to special modes of convergence (convergence in measure, almost everywhere convergence, almost uniform convergence, mean convergence).

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A METRIC ON SPACE OF MEASURABLE FUNCTIONS AND THE RELATED CONVERGENCE

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500109 ◽

2012 ◽

Vol 20 (02) ◽

pp. 211-222 ◽

Cited By ~ 2

Author(s):

GANG LI

Keyword(s):

Measure Theory ◽

Additive Measure ◽

Convergence In Measure ◽

Measurable Functions

A new metric is proposed on the space of measurable functions in the setting of non-additive measure theory. The convergence induced from the metric can be used to describe the convergence in measure for sequences of measurable functions. Furthermore, the space of measurable functions is complete under the metric.

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Absolute Continuity of Fuzzy Measures and Convergence of Sequence of Measurable Functions

Mathematics ◽

10.3390/math8050726 ◽

2020 ◽

Vol 8 (5) ◽

pp. 726

Author(s):

Jun Li

Keyword(s):

Absolute Continuity ◽

General Framework ◽

Type I ◽

Convergence In Measure ◽

Fuzzy Measures ◽

Measurable Functions ◽

Convergent Sequences

In this note, the convergence of the sum of two convergent sequences of measurable functions is studied by means of two types of absolute continuity of fuzzy measures, i.e., strong absolute continuity of Type I, and Type VI. The discussions of convergence a.e. and convergence in measure are done in the general framework relating to a pair of monotone measures, and general results are shown. The previous related results are generalized.

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Onp-Convergence in Measure of a Sequence of Measurable Functions

Abstract and Applied Analysis ◽

10.1155/2011/582576 ◽

2011 ◽

Vol 2011 ◽

pp. 1-7

Author(s):

A. Boccuto ◽

Ch. Papachristodoulos ◽

N. Papanastassiou

Keyword(s):

Equivalence Relation ◽

Metric Space ◽

Quotient Space ◽

Compact Metric Space ◽

Convergence In Measure ◽

Measurable Functions ◽

Natural Way

In the study by Papanastassiou and Papachristodoulos, 2009 the notion ofp-convergence in measure was introduced. In a natural wayp-convergence in measure induces an equivalence relation on the spaceMof all sequences of measurable functions converging in measure to zero. We show that the quotient spaceℳis a complete but not compact metric space.

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On rough convergence of complex uncertain sequences

Journal of Uncertain Systems ◽

10.1142/s1752890921500215 ◽

2021 ◽

Author(s):

Shyamal Debnath ◽

Bijoy Das

Keyword(s):

Complex Numbers ◽

Convergence In Distribution ◽

Convergence In Measure ◽

Uncertain Variables ◽

Measurable Functions ◽

Model Complex ◽

Uncertainty Space ◽

Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. The main purpose of this paper is to introduce rough convergence of complex uncertain sequences and study some convergence concepts namely rough convergence in measure, rough convergence in mean, rough convergence in distribution of complex uncertain sequences. Lastly some relationship between them have been investigated.

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Some Properties Related With L^0 (Ω,F,μ) Space

Al-Qadisiyah Journal Of Pure Science ◽

10.29350/qjps.2020.25.2.1059 ◽

2020 ◽

Vol 25 (2) ◽

pp. 22-26

Author(s):

Asawer Jabar ◽

Noori Al-Mayahi

Keyword(s):

Measure Space ◽

Finite Measure ◽

Convergence In Measure ◽

Measurable Functions ◽

Finite Measure Space ◽

Metric Functions

The purpose of this paper is to investigate elementary properties of these measure and relation between these measure and we define a metric functions on the space of measurable functions and defined on finite measure space and we call the topology induced by p the topology of convergence in measure and we investigate now the connection between the convergence in metric of X and convergence in measure .

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