Henstock integrable functions are Lebesgue integrable on a portion
HTML articles powered by AMS MathViewer
- by Zoltán Buczolich
- Proc. Amer. Math. Soc. 111 (1991), 127-129
- DOI: https://doi.org/10.1090/S0002-9939-1991-1034883-6
- PDF | Request permission
Abstract:
If a real function $f$ defined on an interval $I \subset {{\mathbf {R}}^m}$ is Henstock integrable, then one can always find a nondegenerate subinterval $J \subset I$ on which $f$ is Lebesgue integrable.References
- K. Karták, $K$ teorii vícerozměrného integrálu, Časopis Pešt. Mat. 80 (1955), 400-414.
- Krzysztof M. Ostaszewski, Henstock integration in the plane, Mem. Amer. Math. Soc. 63 (1986), no. 353, viii+106. MR 856159, DOI 10.1090/memo/0353
- Washek F. Pfeffer, The multidimensional fundamental theorem of calculus, J. Austral. Math. Soc. Ser. A 43 (1987), no. 2, 143–170. MR 896622
- W. F. Pfeffer, The divergence theorem, Trans. Amer. Math. Soc. 295 (1986), no. 2, 665–685. MR 833702, DOI 10.1090/S0002-9947-1986-0833702-0 S. Saks, Theory of the integral, Hafner, New York, 1937.
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 127-129
- MSC: Primary 26A39; Secondary 26A42, 28A25
- DOI: https://doi.org/10.1090/S0002-9939-1991-1034883-6
- MathSciNet review: 1034883