@article{1198.46037,
author="Halu\v{s}ka, J\'an and Hutn{\'\i}k, Ondrej",
title="{The general Fubini theorem in complete bornological locally convex
    spaces.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="2",
pages="53-74",
year="2010",
abstract="{This paper is a continuation of the authors' paper [``The Fubini
    theorem for bornological product measures'', Results Math. 54, No.~1--2,
    65--73 (2009; Zbl 1184.46043)]. Here, $X, Y, Z$ are Hausdorff complete
    bornological locally convex spaces with filtering upwards bases of
    bornologies $\mathcal{U}, \mathcal{W}, \mathcal{V}$, respectively; here,
    each $ U \in \mathcal{U}$ is a closed, absolutely convex bounded subset of
    $X$ and $ U \supset U_{0}$ a fixed closed, absolutely convex bounded subset
    of $X$. The subspace of $X$ generated by $U$, with Minkowski functional of
    $U$, is a Banach space $X_{U}$. The topology of $X$ is the inductive limit
    topology of the Banach spaces $\{ X_{U}: U \in \mathcal{U} \}$. Similar
    properties hold for the topologies of $Y, Z$ arising from $\mathcal{W},
    \mathcal{V}$ respectively. $L(X, Y)$ is the space of all continuous linear
    functions from $X$ to $Y$; similarly for $L(Y, Z)$ and $ L(X, Z) $.
 
 $T,
    S$ are two sets, $\bigtriangleup$ and $\bigtriangledown$ are $\delta$-rings
    on $T$ and $S$, respectively, and $m: \bigtriangleup \to L(X, Y)$ and $n:
    \bigtriangledown \to L(Y, Z)$ are two measures. With the help of $(U, W, V)
    \in (\mathcal{U}, \mathcal{W}, \mathcal{V})$, the authors reduce the study
    from complete bornological locally convex spaces $X, Y, Z$ to the Banach
    spaces $X_{U}, Y_{W}, Z_{V}, $. Under certain conditions, an existence
    theorem for the product measure $m \otimes n : \bigtriangleup \otimes
    \bigtriangledown \to L(X, Z)$ is proved. Then under certain conditions, a
    Fubini type theorem is proved for this product measure.}",
reviewer="{Surjit Singh Khurana (Iowa City)}",
keywords="{Fubini theorem; bilinear integral; bornology; locally convex
    topological vector space; product measure; Dobrakov integral}",
classmath="{*46G10 (Vector-valued measures and integration)
28B05 (Vector-valued set functions etc. (measure theory))
}",
}