Applications of the ideals in the measure theory and integration

Doris  DODA; Sokol  SHURDHI

doi:10.24297/jam.v22i.9374

Authors

Doris DODA Department of Economy, Entrepreneurship and Finance, Barleti University
Sokol SHURDHI Department of of Applied and Computer Sciences, Barleti University

DOI:

https://doi.org/10.24297/jam.v22i.9374

Keywords:

∆- convergence in a discrete , ∆- continuity, Weak compactness, Point-wise I -convergence, Symmetric differences, Bohner-type ideal integrals, Weak convergence, Banach spaces, Ideal exhaustiveness

Abstract

In this paper, we will represent some applications to various problems of mass theory and integration, by using the concept of local convergences and exhaustive sequences. We will continue the idea of point-wise I -convergence, Ideal exhaustiveness that was introduced by Komisarski [3], and Kostyrko, Sal´at and Wilczy´nski [4]. The equi-integrable introduced in Bohner-type ideal integrals and a new study on the application of symmetric differences have been presented in the theory of mass and continuous functions, continuing the results of Boccuto, Das, Dimitriou, Papanastassiou [2].

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References

D.Doda , A.Tato, Applications of the ideal in the Bohner type integral, ISC-IMIT 2019 abstract book+cover.pdf Richtmann.org., ISBN:987-1-78911-006-7, 22-23 November 2019.

A. Boccuto, P. Das, X. Dimitriou, N. Papanastassiou, Ideal Exhaustiveness, weak convergence and weak compactness in Banach space, Real analysis Exchange, Vol. 37(2), 2011/2012 pp. 389-410.

A. Komisarski, Pointwise I-convergence and I-convergence in measure of sequences of functions, J. Math. Anal. Appl. 340 (2008), 770–779.

P.Kostyrko, T. Sal´at and W. Wilczy´nski, I-convergence, Real Anal. Exchange 26 (2000–01), 669–685.