On products of almost strong liftings

Abstract

Dealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.

Linear Liftings Respecting Coordinates

“…It has been observed already by Talagrand [10] (see also [6]) that not all liftings have adequate properties from the product point of view. The same holds true in the case of linear liftings.…”

“…densities) to liftings (even those working for products with two factors from [6]) fail for liftings respecting coordinates.…”

On Strong Liftings on Projective Limits

“…The corresponding result for liftings instead of linear liftings can be found in [25,Proposition 2.2].…”

“…[23], [18], [19], [20], [21]) to more general classes of topological probability spaces. In particular, we can extend the class of spaces for which there is a positive answer to a problem of J. Kupka [17] concerning the permanence of the strong lifting property under the formation of products (see Theorem 6.5).…”

Mazur–Orlicz Theorem in Lifting Theory

“…The problem of projecting liftings from product probability spaces into Ž w x. the factors turned up different situations see, e.g., 8,9 . It is know that Ž .…”