On the Strong Liouville Property of Covering Spaces

Topological Spaces with the Strong Skorokhod Property

We study topological spaces with the strong Skorokhod property, i.e., spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measure on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost everywhere convergent sequences of mappings. We construct nonmetrizable spaces with such a proper...

On Holonomy Covering Spaces

Introduction. In [l] L. Markus and the author introduced the concept of holonomy covering spaces for flat affinely connected manifolds or what are also called locally affine spaces. We also proved in [l ] that the holonomy covering space of a complete « dimensional locally affine space must be some « dimensional cylinder, i.e., T^XF"-*, i = 0, •■-,«, where T* denotes the locally affine i dimens...

The Jensen Covering Property

The Jensen covering lemma says that either L has a club class of indiscernibles, or else, for every uncountable set A of ordinals, there is a set B ∈ L with A ⊆ B and card(B) = card(A). One might hope to extend Jensen’s covering lemma to richer weasels, that is, to inner models of the form L[ ~ E] where ~ E is a coherent sequence of extenders of the kind studied in Mitchell-Steel [MiSt]. The pa...

Amenability and the Liouville Property

We present a new approach to the amenability of groupoids (both in the measure theoretical and the topological setups) based on using Markov operators. We introduce the notion of an invariant Markov operator on a groupoid and show that the Liouville property (absence of non-trivial bounded harmonic functions) for such an operator implies amenability of the groupoid. Moreover, the groupoid actio...

Schur-Pair Property and the Structure of Varietal Covering Groups