Statistical convergence in vector lattices

被引：0

作者：

Aydin, A. ^{[1
]}

Temizsu, F. ^{[2
]}

机构：

[1] Mus Alparslan Univ, Dept Math, Mus, Turkiye

[2] Bingol Univ, Dept Math, Bingol, Turkiye

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2023年 / 111卷 / 03期

关键词：

statistical convergence of nets; order convergence; vector lattice; directed set measure; ORDER CONVERGENCE;

D O I：

10.31489/2023M3/4-10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence in vector lattices by using the finite additive measures on directed sets. Moreover, we give some relations between the statistical convergence and the lattice properties such as the order convergence and lattice operators.

引用

页码：4 / 10

页数：7

共 50 条

[1] A MARTINGALE CONVERGENCE THEOREM IN VECTOR LATTICES
DEMARR, R
CANADIAN JOURNAL OF MATHEMATICS, 1966, 18 (02): : 424 - &
[2] GENERALIZATION OF ORDER CONVERGENCE IN THE VECTOR LATTICES
Azar, Kazem Haghnejad
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2022, 37 (03): : 521 - 528
[3] Net convergence structures with applications to vector lattices
O'Brien, M.
Troitsky, V. G.
van der Walt, J. H.
QUAESTIONES MATHEMATICAE, 2023, 46 (02) : 243 - 280
[4] uτ-convergence in locally solid vector lattices
Dabboorasad, Y. A.
Emelyanov, E. Y.
Marabeh, M. A. A.
POSITIVITY, 2018, 22 (04) : 1065 - 1080
[5] ON THE NOTION OF STABILITY OF ORDER CONVERGENCE IN VECTOR LATTICES
GOROKHOVA, SG
EMELYANOV, EY
SIBERIAN MATHEMATICAL JOURNAL, 1994, 35 (05) : 912 - 916
[6] ON STATISTICAL CONVERGENCE IN MODULAR VECTOR SPACES
Nuray, F.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2022, 91 (04): : 377 - 391
[7] Egoroff, σ, and convergence properties in some archimedean vector lattices
Hager, A. W.
van Mill, J.
STUDIA MATHEMATICA, 2015, 231 (03) : 269 - 285
[8] The Brezis-Lieb lemma in convergence vector lattices
Marabeh, Mohammad
TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (03) : 1436 - 1441
[9] RELATIVE UNIFORM CONVERGENCE IN VECTOR LATTICES: ODDS AND ENDS
Emelyanov E.
Journal of Mathematical Sciences, 2023, 271 (6) : 733 - 742
[10] Convergence structures and locally solid topologies on vector lattices of operators
Deng, Yang
de Jeu, Marcel
BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2021, 15 (03)

← 1 2 3 4 5 →