Convergence of ap-Henstock-Kurzweil integral on locally compact spaces

Hemanta Kalita; Ravi P. Agarwal; Bipan Hazarika

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 103-121
  • ISSN: 0011-4642

Abstract

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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, μ ap -Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed.

How to cite

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Kalita, Hemanta, Agarwal, Ravi P., and Hazarika, Bipan. "Convergence of ap-Henstock-Kurzweil integral on locally compact spaces." Czechoslovak Mathematical Journal (2025): 103-121. <http://eudml.org/doc/299910>.

@article{Kalita2025,
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.},
author = {Kalita, Hemanta, Agarwal, Ravi P., Hazarika, Bipan},
journal = {Czechoslovak Mathematical Journal},
keywords = {ap-Henstock-Kurzweil integral; uniformly strong Lusin condition; monotone convergence theorem; $\mu _\{\rm ap\}$-Henstock-Kurzweil equi-integrability; Henstock’s lemma},
language = {eng},
number = {1},
pages = {103-121},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of ap-Henstock-Kurzweil integral on locally compact spaces},
url = {http://eudml.org/doc/299910},
year = {2025},
}

TY - JOUR
AU - Kalita, Hemanta
AU - Agarwal, Ravi P.
AU - Hazarika, Bipan
TI - Convergence of ap-Henstock-Kurzweil integral on locally compact spaces
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 103
EP - 121
AB - 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.
LA - eng
KW - ap-Henstock-Kurzweil integral; uniformly strong Lusin condition; monotone convergence theorem; $\mu _{\rm ap}$-Henstock-Kurzweil equi-integrability; Henstock’s lemma
UR - http://eudml.org/doc/299910
ER -

References

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