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Additivity of integrals on generalized measure spaces. (English) Zbl 0624.28012
A generalized measure space is a triple ($$\Omega$$,$${\mathcal C},\mu)$$ where $$\Omega$$ is a set of $${\mathcal C}$$, a $$\sigma$$-class of subsets of $$\Omega$$ closed with respect to disjoint countable unions and complementation and $$\mu$$ a measure on $${\mathcal C}$$. While in the classical measure theory additivity of integral is an obvious and fundamental result, it is not so in the generalized measure spaces. In general the integral in this case is not additive. The question of the additivity in the case of simple functions is solved in the reviewed paper in a positive way.
Reviewer: T.Neubrunn

##### MSC:
 28C99 Set functions and measures on spaces with additional structure 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 81P20 Stochastic mechanics (including stochastic electrodynamics)
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