Functiones et Approximatio Commentarii Mathematici

On functions that are $BDS$-integrable over convexly bounded vector measures

Iwo Labuda

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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 $X$.

Article information

Funct. Approx. Comment. Math., Volume 50, Number 1 (2014), 151-159.

First available in Project Euclid: 27 March 2014

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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]

convexly bounded vector measure Bartle-Dunford-Schwartz integration spaces of integrable functions $\sigma$-Lebesgue property $\sigma$-Levi property


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.

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