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
University of Louisville, Department of Mathematics, Louisville 40292, KY, USA
Received 6 February 1987; Revised 15 March 1987
Copyright © 1988 Krzysztof Ostaszewski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.