A multidimensional integration by parts formula for the Henstock-Kurzweil integral

Tuo-Yeong Lee

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 1, page 63-74
  • ISSN: 0862-7959

Abstract

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It is shown that if g is of bounded variation in the sense of Hardy-Krause on ∏ i = 1 m [ a i , b i ] , then g χ ∏ i = 1 m ( a i , b i ) is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.

How to cite

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Lee, Tuo-Yeong. "A multidimensional integration by parts formula for the Henstock-Kurzweil integral." Mathematica Bohemica 133.1 (2008): 63-74. <http://eudml.org/doc/32577>.

@article{Lee2008,
abstract = {It is shown that if $g$ is of bounded variation in the sense of Hardy-Krause on $\{\mathop \{\prod \}\limits _\{i=1\}^\{m\}\} [a_i, b_i]$, then $g \chi _\{ _\{\{\mathop \{\prod \}\limits _\{i=1\}^\{m\}\} (a_i, b_i)\}\}$ is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.},
author = {Lee, Tuo-Yeong},
journal = {Mathematica Bohemica},
keywords = {Henstock-Kurzweil integral; bounded variation in the sense of Hardy-Krause; integration by parts; Henstock-Kurzweil integral; bounded variation in the sense of Hardy-Krause; integration by parts},
language = {eng},
number = {1},
pages = {63-74},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A multidimensional integration by parts formula for the Henstock-Kurzweil integral},
url = {http://eudml.org/doc/32577},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Lee, Tuo-Yeong
TI - A multidimensional integration by parts formula for the Henstock-Kurzweil integral
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 1
SP - 63
EP - 74
AB - It is shown that if $g$ is of bounded variation in the sense of Hardy-Krause on ${\mathop {\prod }\limits _{i=1}^{m}} [a_i, b_i]$, then $g \chi _{ _{{\mathop {\prod }\limits _{i=1}^{m}} (a_i, b_i)}}$ is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.
LA - eng
KW - Henstock-Kurzweil integral; bounded variation in the sense of Hardy-Krause; integration by parts; Henstock-Kurzweil integral; bounded variation in the sense of Hardy-Krause; integration by parts
UR - http://eudml.org/doc/32577
ER -

References

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