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On Kurzweil-Henstock equiintegrable sequences. (English) Zbl 0863.26009

Summary: The concept of equiintegrability of a sequence of Kurzweil-Henstock integrable functions is a tool for deriving a relatively strong type of convergence theorem for the Kurzweil-Henstock integral. In terms of convergences of some integrals conditions for equiintegrability of a sequence of Kurzweil-Henstock integrable functions are given. The results show in some sense how far equiintegrability is from being a necessary and sufficient condition for convergence of integrals for pointwise convergent sequences of integrable functions.

MSC:

26A39 Denjoy and Perron integrals, other special integrals
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