1 citations · 1 across the 8 of their papers we have counts for
9 papers
Loeb Extension and Loeb Equivalence II
Duanmu Haosui, David Schrittesser, William Weiss
The paper answers two open questions that were raised in by Keisler and Sun. The first question asks, if we have two Loeb equivalent spaces and $(Ω, \mathcal G…
Finitely-additive, countably-additive and internal probability measures
Haosui Duanmu, William Weiss
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an inte…
Loeb Extension and Loeb Equivalence
Robert M. Anderson, Haosui Duanmu, David Schrittesser +1
In Keisler and Sun (2004), the authors raise several open problems on Loeb equivalences between various internal probability spaces. We provide counter-examples for the first two o…
On the tightness of -modifications
Alan Dow, István Juhász, Lajos Soukup +2
The -modification of a topological space is the space on the same underlying set generated by, i.e. having as a basis, the collection of all subsets of . Be…
Generalized symmetric systems and thin-very tall compact scattered spaces
Miguel Angel Mota, William Weiss
We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal , there…
Universal Functions
Paul B. Larson, Arnold W. Miller, Juris Steprans +1
A function of two variables F(x,y)is universal iff for every other function G(x,y) there exists functions h(x) and k(y) with G(x,y) = F(h(x),k(y)) Sierpinski showed that assuming t…
The counterparts to statements that are equivalent to the Continuum Hypothesis
Asger Tornquist, William Weiss
We consider natural definable analogues of many of the classical statements that have been shown to be equivalent to CH. It is shown that these analogues are equiva…
Definable Davies' Theorem
Asger Tornquist, William Weiss
We prove the following analogue of a Theorem of R.O. Davies: Every function can be represented as a sum of rectangular functions if and only if…
Steinhaus Sets and Jackson Sets
Su Gao, Arnold W. Miller, William A. R. Weiss
We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point. We give a complete characterizat…