Abstract
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.
Keywords
- Unit Cube
- Continuous Linear
- Compact Hausdorff Space
- Derivation Base
- Part Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This author was partially supported by a University of Louisville research grant.
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© 1990 Springer-Verlag
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Mikusiński, P., Ostaszewski, K. (1990). The space of Henstock integrable functions II. In: Bullen, P.S., Lee, P.Y., Mawhin, J.L., Muldowney, P., Pfeffer, W.F. (eds) New Integrals. Lecture Notes in Mathematics, vol 1419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083105
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DOI: https://doi.org/10.1007/BFb0083105
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