New Integrals pp 136-149 | Cite as

The space of Henstock integrable functions II

  • Piotr Mikusiński
  • Krzysztof Ostaszewski
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1419)


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 
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.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Piotr Mikusiński
    • 1
  • Krzysztof Ostaszewski
    • 2
  1. 1.Department of MathematicsUniversity of Central Florida
  2. 2.Department of MathematicsUniversity of LouisvilleLouisville

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