Czechoslovak Mathematical Journal, first online, pp. 1-19
Convergence of ap-Henstock-Kurzweil integral on locally compact spaces
Hemanta Kalita, Ravi P. Agarwal, Bipan Hazarika
Received October 6, 2022. Published online June 19, 2023.
Abstract: We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, $\mu_{\rm ap}$-Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.
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Affiliations: Hemanta Kalita (corresponding author), Department of Mathematics, Assam Don Bosco University, Tapesia Gardens, Kamarkuchi, Sonapur, Assam 782402, India, e-mail: hemanta30kalita@gmail.com; Ravi P. Agarwal, Department of Mathematics, Texas A& M University-Kingsville, 700 University Blvd, Kingsville, TX 78363, USA, e-mail: Ravi.Agarwal@tamuk.edu; Bipan Hazarika, Department of Mathematics, Gauhati University, Guwahati, Assam 781014, India, e-mail: bh_rgu@yahoo.co.in
