On the associativity of the product of measure spaces

If we arbitrarily choose finitely many measure spaces, then the existence of a product of these measure spaces can be proved. It is well known that this operation is not associative which is a substantial difficulty. In this paper we show that the associative law remains true between the σ-algebras of the product spaces, and we give an extension of the Fubini's theorem. This revised version was published online in June 2006 with corrections to the Cover Date.