Functions and measures on products spaces

On products of almost strong liftings

“…By the claim W(co) c PiC2C(co,9)) n E, ^( 0 ) c p 2 (<%(co,9)) n rjo,,. This implies p 1 (^'(a),9)) n E = ,0)) 0^ = ^( 0 N. D. Macheras and W. Strauss [14] ty (,u…”

“…Before stating the first theorem we mention that the product of Baire probability spaces is in general not a Baire probability space (see [2]), and the same is true for topological probability spaces (see [8]), where the situation is even much worse (see [18 and 19]). For this reason we assume in the next theorem only the Baire-ASLP for the product which is more likely satisfied than the ASLP.…”

“…According to [30] , 9)) n E is again an ultrafilter in E and so is ^(co) = &(co), p 2 ('^(co, 9)) n rjoc is an ultrafilter in r)^ and so is ty (9). By the claim W(co) c PiC2C(co,9)) n E, ^( 0 ) c p 2 (<%(co,9)) n rjo,,.…”

“…By induction it is again sufficient to give the proof for n = 2 and for simplicity we may put i = 1. We denote by p\(co) := a^ forw = (ct) u a) 2 [23]). Since p is almost strong by assumption there exists a Q. o e E with AI(£2 0 ) = 1 such that…”

Product of uniform measures

“…)dµ 2 . Then g ∈ C ub (X 1 ) and µ, ν, defined by µ( f ) = ( f dµ 2 )dµ 1 and ν( f ) = ( f dµ 1 )dµ 2 are in M u (X 1 × X 2 ) and µ = ν on C ub (X 1 ) ⊗ C ub (X 2 ). (1, 2)).…”