Real Analysis Exchange
- Real Anal. Exchange
- Volume 29, Number 2 (2003), 763-780.
On McShane integrability of Banach space-valued functions.
The McShane integral of Banach space-valued functions $f:I\to X$ defined on an $m$-dimensional interval $I$ is considered in this paper. We show that a McShane integrable function is integrable over measurable sets contained in $I$ (Theorem 9). A certain type of absolute continuity of the indefinite McShane integral with respect to Lebesgue measure is derived (Theorem 11) and we show that the indefinite McShane integral is countably additive (Theorem 16). Allowing more general partitions using measurable sets instead of intervals another McShane type integral is defined and we show that it is equivalent to the original McShane integral (Theorem 21)
Real Anal. Exchange, Volume 29, Number 2 (2003), 763-780.
First available in Project Euclid: 7 June 2006
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22] 26A39: Denjoy and Perron integrals, other special integrals
Kurzweil, Jaroslav; Schwabik, Štefan. On McShane integrability of Banach space-valued functions. Real Anal. Exchange 29 (2003), no. 2, 763--780. https://projecteuclid.org/euclid.rae/1149698538