Scale-invariant measurability in abstract Wiener spaces

An Infinitesimal Approach to Stochastic Analysis on Abstract Wiener Spaces

On Measurability over Product Spaces

The main result announced here is a negative solution of the Kakutani-Doob problem [3 ] on measurability of stochastic processes, assuming the continuum hypothesis. Thus the positive solution proposed earlier by M. Mahowald [ó] is incorrect (the last step in the argument applies the Fubini theorem to sets in a product space which need not be measurable). Complete proofs will appear in the Proce...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Non-measurability properties of interpolation vector spaces

It is known that every dimension group with order-unit of size at most א1 is isomorphic to K0(R) for some locally matricial ring R (in particular, R is von Neumann regular); similarly, every conical refinement monoid with order-unit of size at most א1 is the image of a V-measure in Dobbertin’s sense, the corresponding problems for larger cardinalities being open. We settle these problems here, ...

Stepanov’s Theorem in Wiener spaces

One generalization of this result has been given in [BRZ], when the domain X is a metric measure space. In this case, the authors deal with metric spaces endowed with a doubling measure and supporting Poincaré-type inequalities. Both conditions ensure the existence of a strong measurable differentiable structure on the space X which provides a differentiation theory for Lipschitz functions in t...