L2-TORSION, THE MEASURE-THEORETIC DETERMINANT CONJECTURE, AND UNIFORM MEASURE EQUIVALENCE

L-torsion and Bounded Measure Equivalence of Groups

We show that the L-torsion of finite aspherical CW-complexes with boundedly measure equivalent fundamental groups agrees up to a factor given by the index of the measure equivalence.

Dynamic equivalence relation on the fuzzy measure algebras

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

Torsion without the Determinant Class Condition and Extended L2 Cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of ...

Measure Theoretic Probability

Preface In these notes we explain the measure theoretic foundations of modern probability. The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics and prob...

Measure-Theoretic Probability I