Flows in Infinite-Dimensional Phase Space Equipped with a Finitely-Additive Invariant Measure

Representing Finitely Additive Invariant Probabilities

A Note on Invariant Finitely Additive Measures

We show that under certain general conditions any finitely additive measure which is defined for all subsets of a set X and is invariant under the action of a group G acting on X is concentrated on a G-invariant subset Y on which the G-action factors to that of an amenable group. The result is then applied to prove a conjecture of S. Wagon about finitely additive measures on spheres. It is well...

Lebesgue measure in the infinite - dimensional space ?

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional

Infinite Previsions and Finitely Additive Expectations

We give an extension of de Finetti’s concept of coherence to unbounded (but real-valued) random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of th...

Infinite dimensional finitely forcible graphon

Graphons are analytic objects associated with convergent sequences of dense graphs. Problems from extremal combinatorics and theoretical computer science led to a study of finitely forcible graphons, i.e., graphons determined by finitely many subgraph densities. Lovász and Szegedy conjectured that the topological space of typical vertices of such a graphon always has finite dimension, which wou...