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Keywords:
equiintegrable sequence; Kurzweil-Henstock integral
Summary:
For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation \lim_{m \to\infty}\int_a^bf_m(s)\dd s = \int_a^b\lim_{m \to\infty}f_m(s)\dd s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.
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