From Arzelà–Ascoli to Riesz–Kolmogorov

Przemysław Górka; Humberto Rafeiro

doi:10.1016/j.na.2016.06.004

From Arzelà–Ascoli to Riesz–Kolmogorov

Przemysław Górka
, Humberto Rafeiro

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.

Original language	English
Pages (from-to)	23-31
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	144
DOIs	https://doi.org/10.1016/j.na.2016.06.004
Publication status	Published - Oct 1 2016
Externally published	Yes

Keywords

Banach function spaces
Grand variable exponent Lebesgue spaces
Metric measure spaces
Riesz–Kolmogorov theorem

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2016.06.004

Cite this

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abstract = "In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.",

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AU - Rafeiro, Humberto

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N2 - In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.

AB - In this paper we study totally bounded sets in Banach function spaces (BFS), from which we characterize compact sets (via Hausdorff criterion) in some non-standard function spaces which fall under the umbrella of BFS. We obtain a Riesz–Kolmogorov compactness theorem for the grand variable exponent Lebesgue spaces.

KW - Banach function spaces

KW - Grand variable exponent Lebesgue spaces

KW - Metric measure spaces

KW - Riesz–Kolmogorov theorem

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

From Arzelà–Ascoli to Riesz–Kolmogorov

Abstract

Keywords

ASJC Scopus subject areas

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