The space of Henstock integrable functions of two variables. (1988)

• Record Type: Journal Article
• Authors: Ostaszewski, Krzysztof
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 11:Number 1(1988)
• Page Start: 15
• Page End: 21
• Publication Date: 1988
• Subjects: Henstock integral -- barrel -- barrelled space -- normed space -- continuous linear functionals; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171288000043
• Languages: English
• ISSNs: 0161-1712

Abstract

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.