Compactly uniform Bochner integrability of random elements

Ünver, Mehmet; Uluçay, Havva

doi:10.1007/s11117-017-0465-1

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Following two propositions show that the concept of weak A-bounded uniform integrability generalizes the concepts of weak uniform integrability of [11] and A-compact uniform Bochner integrability of [20], respectively. Proposition 2.9.…”

Section: Weak Uniformly Integrability Of Sequences Of Random Elementsmentioning

confidence: 92%

“…However, convergence in probability is equivalent to mean convergence under the uniform integrability condition. Various types of uniform integrability can be found in [1,4,[15][16][17][18]20].…”

Section: Introductionmentioning

confidence: 99%

“…The concept of A-compact uniform integrability was generalized via Bochner integral by Unver and Uluçay [20]. Let (Y, ∥.∥) be a separable Banach space.…”

Section: Introductionmentioning

confidence: 99%

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Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals

Uluçay

Ünver

2023

Hacettepe Journal of Mathematics and Statistics

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In probability theory, uniform integrability of families of random variables or random elements plays an important role in the mean convergence. In this paper, we introduce a new version of uniform integrability for sequences in normed spaces in the weak sense. We study the relationship of this new concept with summability theory by considering statistical convergence. We also define a new type of uniform integrability of random elements taking values in topological vector spaces by considering weak integrals. Moreover, we study the connection of summability theory with this new concept as well.

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Section: Weak Uniformly Integrability Of Sequences Of Random Elementsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals

Uluçay

Ünver

2023

Hacettepe Journal of Mathematics and Statistics

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$$\boldsymbol{q}$$-Rung Orthopair Fuzzy Normed Spaces and Statistical Convergence

Uluçay

2024

Lobachevskii J Math

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A Korovkin Type Approximation Theorem For Balázs Type Bleimann, Butzer and Hahn Operators via Power Series Statistical Convergence

Söylemez

2022

Mathematica Slovaca

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In this paper, we obtain a Korovkin type approximation theorem for power series statistical convergence of functions belonging to the class produced by multivariable modulus of continuity function. As an application of this theorem, we construct a non-tensor product Balázs type BBH operator which does not converge in ordinary sense. Moreover, we study promised approximation properties of this operator and compute the rate of convergence. Finally, we prove that our new approximation result works but its classical case fails.

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Compactly uniform Bochner integrability of random elements

Cited by 3 publications

References 13 publications

Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals

Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals

$$\boldsymbol{q}$$-Rung Orthopair Fuzzy Normed Spaces and Statistical Convergence

A Korovkin Type Approximation Theorem For Balázs Type Bleimann, Butzer and Hahn Operators via Power Series Statistical Convergence

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