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The Lebesgue decomposition theorem for generalized measures. (English) Zbl 1009.28014
Generalized measures in the sense of E. P. Klement and S. Weber [Fuzzy Sets Syst. 40, No. 2, 375-394 (1991; Zbl 0733.28012)], i.e., measures defined on a $$\sigma$$-complete lattice and with values in a $$\sigma$$-complete lattice ordered commutative semigroup are considered. A theorem of Lebesgue type decomposition for such measures is proved under the additional assumption that the lattice in the domain has the so-called relative complement property.
##### MSC:
 2.8e+11 Fuzzy measure theory
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