proof of equivalent definitions of analytic sets for measurable spaces
is -analytic (http://planetmath.org/AnalyticSet2).
is the projection (http://planetmath.org/GeneralizedCartesianProduct) of a set onto .
Here, denotes the product -algebra (http://planetmath.org/ProductSigmaAlgebra) of and .
(1) implies (2): Let denote the paving consisting of the closed subsets of . If is -analytic then there exists a set such that , where is the projection map (see proof of equivalent definitions of analytic sets for paved spaces). In particular, implies that is contained in the -algebra .
|Title||proof of equivalent definitions of analytic sets for measurable spaces|
|Date of creation||2013-03-22 18:48:41|
|Last modified on||2013-03-22 18:48:41|
|Last modified by||gel (22282)|