On Kurzweil-Henstock equiintegrable sequences

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

Full text of the article:

• Compressed Postscript file (338279 Bytes)