Additivity of integrals on generalized measure spaces.

*(English)*Zbl 0624.28012A 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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\textit{J. E. Zerbe} and \textit{S. P. Gudder}, J. Comb. Theory, Ser. A 39, 42--51 (1985; Zbl 0624.28012)

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