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Keywords:
ap-Henstock-Kurzweil integral; uniformly strong Lusin condition; monotone convergence theorem; $\mu _{\rm ap}$-Henstock-Kurzweil equi-integrability; Henstock's lemma
ap-Henstock-Kurzweil integral; uniformly strong Lusin condition; monotone convergence theorem; $\mu _{\rm ap}$-Henstock-Kurzweil equi-integrability; Henstock's lemma
Summary:
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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