Gradients of Borel functions
A concept of absolute continuity and a Riemann type integral
We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.
A full descriptive definition of the BV-integral
We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral.
Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions
We study the integrability of Banach valued strongly measurable functions defined on . In case of functions given by , where belong to a Banach space and the sets are Lebesgue measurable and pairwise disjoint subsets of , there are well known characterizations for the Bochner and for the Pettis integrability of (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
Page 1