Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 50, Number 1 (2014), 151-159.
On functions that are $BDS$-integrable over convexly bounded vector measures
Spaces of scalar functions that are integrable in the sense of Bartle-Dunford-Schwartz integration, with respect to a~convexly bounded vector measure $\mu$, are studied. For instance, under the assumption that the range space $X$ of $\mu$ is sequentially complete, the effect of the Orlicz-Pettis property (with respect to a weaker topology on $X$) on the size of $L^1(\mu)$ is investigated. Some completeness properties of the space $L^1_\bullet(\mu)$ of `scalarly integrable functions' are established for general $X$.
Funct. Approx. Comment. Math., Volume 50, Number 1 (2014), 151-159.
First available in Project Euclid: 27 March 2014
Permanent link to this document
Digital Object Identifier
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]
Secondary: 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
Labuda, Iwo. On functions that are $BDS$-integrable over convexly bounded vector measures. Funct. Approx. Comment. Math. 50 (2014), no. 1, 151--159. doi:10.7169/facm/2014.50.1.4. https://projecteuclid.org/euclid.facm/1395924288