The space of Henstock integrable functions on the unit cube in the m-dimensional Euclidean space is normed, barrelled, and not complete. We describe its completion in the space of Schwartz distributions.
We also show how the distribution functions for finite signed Borel measures are multipliers for the Henstock integrable functions, and how they generate continuous linear functionals on the space of Henstock integrable functions. Finally, we discuss various integration by parts formulas for the two-dimensional Henstock integral.
Unit Cube Continuous Linear Compact Hausdorff Space Derivation Base Part Formula
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