Glasnik Matematicki, Vol. 61, No. 1 (2026), 17-57. \( \)

ON THE NOTION OF APPROXIMATELY LOWER PRE-OSCILLATORY SEQUENCES OF FUNCTIONS

Andrija Raguž

Department of Economics and Mathematics, Zagreb School of Economics and Management, Filipa Vukasovića 1, 10 000 Zagreb, Croatia
e-mail:araguz@zsem.hr

Abstract.   In this paper we introduce the notion of an approximately lower pre-oscillatory (app LPO, for brevity) sequence of functions. When the domain is a compact interval and the sequence consists of absolutely continuous functions, a similar notion is introduced in the paper [26]. The generalization considered herein is twofold. On the one hand, we consider the case of a domain which is a measurable set of possibly infinite measure, and, on the other, we consider the case of a sequence of measurable functions. We adapt the definition accordingly, and we present some properties of the aforementioned notion of an app LPO sequence of functions. In particular, we study the cases when such an app LPO property is preserved under the outer or the inner composition with a suitable class of functions.

2020 Mathematics Subject Classification.   26A99, 28A20, 28E99, 49J45

Key words and phrases.   Measurability, Banach indicatrix, approximate limit, bounded variation, absolute continuity

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https://doi.org/10.3336/gm.61.1.02

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