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, cilt.179, sa.1, ss.121-132, 2025 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 179 Sayı: 1
  • Basım Tarihi: 2025
  • Dergi Adı: Transactions of A. Razmadze Mathematical Institute
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.121-132
  • Anahtar Kelimeler: Dunford–Pettis integrals, Riemann–Lebesgue integrals, Vector measure, Weakly Riemann–Lebesgue integrals
  • Uşak Üniversitesi Adresli: Evet

Özet

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.