A REPRESENTATION THEOREM OF A RIEMANN–LEBESGUE INTEGRABLE FUNCTION ASSOCIATED WITH A VECTOR MEASURE

Kalita H., Agarwal R. P., SAVAŞ E.

Transactions of A. Razmadze Mathematical Institute, vol.179, no.1, pp.121-132, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 179 Issue: 1
  • Publication Date: 2025
  • Journal Name: Transactions of A. Razmadze Mathematical Institute
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.121-132
  • Keywords: Dunford–Pettis integrals, Riemann–Lebesgue integrals, Vector measure, Weakly Riemann–Lebesgue integrals
  • Uşak University Affiliated: Yes

Abstract

We study several properties of the Banach lattice RL 1(m, X ) of Riemann–Lebesgue integrable function space associated with a vector measure m. We also introduce weakly RL-integrable function spaces endowed with a vector measure. A representation of the weakly Riemann–Lebesgue integral in terms of unconditionally convergent series is given. Finally, we discuss a weakly Riemann–Lebesgue integral that must coincide with the Bochner integral only if the series is absolutely convergent. In application, the conditional expectation of a weakly RL-integrable function is shown.