More generally, the product -algebra can be defined for an arbitrary number of measurable spaces , where runs over an index set . The product is the -algebra on the generalized cartesian product generated by sets of the form where for all , and for all but finitely many . If are the projection maps, then this is the smallest -algebra with respect to which each is measurable (http://planetmath.org/MeasurableFunctions).
|Date of creation||2013-03-22 18:47:21|
|Last modified on||2013-03-22 18:47:21|
|Last modified by||gel (22282)|