MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 189-207, 1996

On Kurzweil-Henstock equiintegrable sequences

Stefan Schwabik, Ivo Vrkoc

Stefan Schwabik, Ivo Vrkoc, Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:

Abstract: 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.

Keywords: equiintegrable sequences, Kurzweil-Henstock integral

Classification (MSC91): 26A39

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