Abstract Given a purely non-atomic, finite measure space $$(\Omega ,\Sigma ,\nu )$$ ( Ω , Σ ν ) , it is proved that for every closed, infinite-dimensional subspace V of $$L_p(\nu L</m...

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...

We show that it is consistent, relative to ω many supercompact cardinals, that the super tree property holds at אn for all 2 ≤ n < ω but there are weak square and a very good scale at אω .

The notion of strong p-Helly hypergraphs was introduced by Golumbic and Jamison in 1985 [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, J. Combin. Theory Ser. B 38 (1985) 8–22]. Independently, other authors [A. Bretto, S. Ubéda, J. Žerovnik, A polynomial algorithm for the strong Helly property. Inform. Process. Lett. 81 (2002) 55–57, E. Prisner, Hereditary clique-...

Let (X1, . . . , Xd) be a random nonnegative integer vector. Many conditions are known to imply a central limit theorem for a sequence of such random vectors, for example, independence and convergence of the normalized covariances, or various combinatorial conditions allowing the application of Stein’s method, couplings, etc. Here, we prove a central limit theorem directly from hypotheses on th...