Another Perron type integration in n dimensions as an extension of integration of stepfunctions

Jiří Jarník; Jaroslav Kurzweil

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 3, page 557-575
  • ISSN: 0011-4642

Abstract

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For a new Perron-type integral a concept of convergence is introduced such that the limit f of a sequence of integrable functions f k , k ∈ ℕ is integrable and any integrable f is the limit of a sequence of stepfunctions g k , k ∈ ℕ .

How to cite

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Jarník, Jiří, and Kurzweil, Jaroslav. "Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions." Czechoslovak Mathematical Journal 47.3 (1997): 557-575. <http://eudml.org/doc/30383>.

@article{Jarník1997,
abstract = {For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_k$, $ k \in \mathbb \{N\}$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_k$, $ k \in \mathbb \{N\}$.},
author = {Jarník, Jiří, Kurzweil, Jaroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {Perron-type integral; equiconvergence},
language = {eng},
number = {3},
pages = {557-575},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions},
url = {http://eudml.org/doc/30383},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Jarník, Jiří
AU - Kurzweil, Jaroslav
TI - Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 557
EP - 575
AB - For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_k$, $ k \in \mathbb {N}$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_k$, $ k \in \mathbb {N}$.
LA - eng
KW - Perron-type integral; equiconvergence
UR - http://eudml.org/doc/30383
ER -

References

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  1. Perron-type integration on n -dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence, Czechosl. Math. J. 46 (121) (1996), 1–20. (1996) MR1371683
  2. Perron-type integration on n -dimensional intervals and its properties, Czechosl. Math. J. 45 (1995), 79–106. (1995) MR1314532
  3. Nichtabsolut konvergente Integrale, Teubner, Leipzig, 1980. (1980) Zbl0441.28001MR0597703
  4. A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals, Mem. Amer. Math. Soc. 88 (1969), . (1969) Zbl0188.35702MR0265527
  5. Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields, Czechosl. Math. J. 31 (1981), 614–632. (1981) Zbl0562.26004MR0631606
  6. Unified Integration, Academic Press, 1983. (1983) Zbl0551.28001MR0740710

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