⋄α-Measurability and combined measure theory on time scales. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Wang, Chao; Qin, Guangzhou; Agarwal, Ravi P.; O'Regan, Donal
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 2755
• Page End: 2796
• Publication Date: 2022-05-24
• Subjects: Measure theory -- ◊α-measurability -- ◊α-measurable functions -- ◊α-integral -- time scales; 26E70 -- 28A12 -- 28A25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1820997
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we introduce the concept of ◊ α -measurability and establish the combined measure theory on time scales. Particularly, one can obtain Δ-measure theory and ∇-measure theory on time scales by letting α = 1 and α = 0, respectively. Moreover, some criteria for ◊ α -measurability of a set are obtained and the notion of Lebesgue ◊ α -measurable functions is introduced and studied. Based on it, the Lebesgue ◊ α -integral and Riemann ◊ α -integral are introduced and the relation between them is discussed.