On basic summability in $ \mathbb{R} $

B. Sarić

Faculty of Technical Sciences, University of Kragujevac, Svetog Save 65, 32 000, Čačak, Serbia

Abstract: The paper deals with the concept of basic summability of residue function of interval function, which is a synonym for its differential form. As one comprehensive concept, it includes not only all known concepts of integrability, such as Newton's, generalized Riemann and generalized Riemann — Stieltjes integrability, but also arithmetic series.

Keywords: basic summability, total integrability.

MSC: 26A39, 26A42, 26A46, 26E25

Received: 17.07.2024

Language: English

 English version: Ufa Mathematical Journal, 2025, 17:3, 137–148