International Journal of Mathematics and Mathematical Sciences 
Volume 11 (1988), Issue 1, Pages 15-21
doi:10.1155/S0161171288000043

The space of Henstock integrable functions of two variables

Krzysztof Ostaszewski

 University of Louisville, Department of Mathematics, Louisville 40292, KY, USA
Received 6 February 1987; Revised 15 March 1987

Abstract

We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions.