On rough convergence of complex uncertain sequences

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.

Convergence of Complex Uncertain Double Sequences

2020 ◽  
Vol 16 (03) ◽  
pp. 447-459 ◽  
Author(s):  
Debasish Datta ◽  
Binod Chandra Tripathy
Keyword(s):  
Complex Numbers ◽  
Convergence In Distribution ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Mean Convergence ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
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. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

Statistical Convergence of Complex Uncertain Sequences

2017 ◽  
Vol 13 (03) ◽  
pp. 359-374 ◽  
Author(s):  
Binod Chandra Tripathy ◽  
Pankaj Kumar Nath
Keyword(s):  
Statistical Convergence ◽  
Complex Numbers ◽  
Convergence In Distribution ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Decomposition Theorems ◽  
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. This paper introduces the statistical convergence concepts of complex uncertain sequences: statistical convergence almost surely (a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) In addition, decomposition theorems and relationships among them are discussed.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

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.

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

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.

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

Positivity ◽  
2008 ◽  
Vol 13 (1) ◽  
pp. 243-253 ◽  
Author(s):  
Nikolaos Papanastassiou ◽  
Christos Papachristodoulos
Keyword(s):  
Minimal Elements ◽  
Convergence In Measure ◽  
Measurable Functions

scholarly journals Spaces of measurable functions

2013 ◽  
Vol 11 (7) ◽  
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.

Distance of convergence in measure on spaces of measurable functions

Positivity ◽  
2018 ◽  
Vol 23 (3) ◽  
pp. 507-521
Author(s):  
Mehmet Unver ◽  
Sevda Sagiroglu
Keyword(s):  
Convergence In Measure ◽  
Measurable Functions

scholarly journals On rough convergence variables of triple sequences

Analysis ◽  
2020 ◽  
Vol 40 (2) ◽  
pp. 85-88
Author(s):  
Nagarajan Subramanian ◽  
Ayhan Esi
Keyword(s):  
Convergence In Distribution ◽  
Fundamental Theory ◽  
Mathematical Properties ◽  
Convergence Almost Surely ◽  
The Relationship ◽  
Convergence In Mean

AbstractTriple sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper contains four types of convergence concepts, namely, convergence almost surely, convergence incredibility, trust convergence in mean, and convergence in distribution, and discuss the relationship among them and some mathematical properties of those new convergence.

Autocontinuity, convergence in measure, and convergence in distribution

1997 ◽  
Vol 92 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Toshiaki Murofushi ◽  
Michio Sugeno ◽  
Manabu Suzaki
Keyword(s):  
Convergence In Distribution ◽  
Convergence In Measure

scholarly journals A note on convergence in measure and selection principles

Filomat ◽  
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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