The sharp Riesz-type definition for the Henstock-Kurzweil integral.
Lee, Tuo-Yeong
Real Anal. Exchange, Tome 28 (2002) no. 1, p. 55-71 / Harvested from Project Euclid
In this paper, we prove that if $f$ is Henstock-Kurzweil integrable on a compact subinterval $[a,b]$ of the real line, then the following conditions are satisfied: (i) there exists an increasing sequence $\{X_n\}$ of closed sets whose union is $[a,b]$; (ii) $\{f{\chi_{ _{X_n}}}\}$ is a sequence of Lebesgue integrable functions on $[a,b]$; (iii) the sequence $\{f{\chi_{ _{X_n}}}\}$ is Henstock-Kurzweil equi-integrable on $[a,b]$. Subsequently, we deduce that the gauge function in the definition of the Henstock-Kurzweil integral can be chosen to be measurable, and an indefinite Henstock-Kurzweil integral generates a sequence of uniformly absolutely continuous finite variational measures.
Publié le : 2002-05-14
Classification:  Henstock-Kurzweil integral,  equi-integrability,  26A39
@article{1150118735,
     author = {Lee, Tuo-Yeong},
     title = {The sharp Riesz-type definition for the Henstock-Kurzweil integral.},
     journal = {Real Anal. Exchange},
     volume = {28},
     number = {1},
     year = {2002},
     pages = { 55-71},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150118735}
}
Lee, Tuo-Yeong. The sharp Riesz-type definition for the Henstock-Kurzweil integral.. Real Anal. Exchange, Tome 28 (2002) no. 1, pp.  55-71. http://gdmltest.u-ga.fr/item/1150118735/