In mathematics, the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by Kolmogoroff (1930) including the Lebesgue–Stieltjes integral, the Burkill integral, and the Hellinger integral as special cases. The integral is a limit over a directed family of partitions, when the resulting limiting value is independent of the tags of each partition segment.
References[edit]
- "On integration in Banach spaces, VI", Ivan Dobrakov and Pedro Morales, Czechoslovak Mathematical Journal, 35 (1985), #2, 173-187, doi:10.21136/CMJ.1985.102009, MR787123.
- "On integration in Banach spaces, VII", Ivan Dobrakov, Czechoslovak Mathematical Journal, 38 (1988), #3, 434-449, doi:10.21136/CMJ.1988.102239, MR950297.
- Kolmogoroff, A. (1930), "Untersuchungen über den Integralbegriff", Mathematische Annalen, 103 (1): 654–696, doi:10.1007/BF01455714, ISSN 0025-5831
- Skvortsov, V. A. (2001) [1994], "Kolmogorov integral", Encyclopedia of Mathematics, EMS Press