Abstract
In this paper we first give an axiomatic definition of a fuzzy σ-algebra which is a generalisation of the family of fuzzy events considered by L.A. Zadeh [13]. The relationship between classical and fuzzy σ-algebras and between topologies and σ-algebras, in both cases, classical and fuzzy, is established in the notation of commutative diagrams. For fuzzy topologies we refer to the work of R. Lowen [8]. After a comparison between classical measurability of functions and fuzzy measurability defined in this paper we finally introduce the product of fuzzy σ-algebras.
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