### Projective limits of perfect measure spaces

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Given two measure spaces equipped with liftings or densities (complete if liftings are considered) the existence of product liftings and densities with lifting invariant or density invariant sections is investigated. It is proved that if one of the marginal liftings is admissibly generated (a subclass of consistent liftings), then one can always find a product lifting which has the property that all sections determined by one of the marginal spaces are lifting invariant (Theorem 2.13). For a large...

We study the integrability of Banach space valued strongly measurable functions defined on $[0,1]$. In the case of functions $f$ given by ${\sum}_{n=1}^{\infty}{x}_{n}{\chi}_{{E}_{n}}$, where ${x}_{n}$ are points of a Banach space and the sets ${E}_{n}$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for Bochner and Pettis integrability of $f$. The function $f$ is Bochner integrable if and only if the series ${\sum}_{n=1}^{\infty}{x}_{n}\left|{E}_{n}\right|$ is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of $f$....

We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by ${\sum}_{n=1}^{\infty}{x}_{n}{\chi}_{{E}_{n}}$, where ${x}_{n}$ belong to a Banach space and the sets ${E}_{n}$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.

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