Radiation reaction, renormalization and Poincaré symmetry.
Radon measures
Radon Measures on Banach Spaces with their Weak Topologies
The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.
Radon Nikodym property and set-valued integration
Radon spaces which are not -fragmentable
Radon-Nikodym derivatives and conditioning in fuzzy measure theory.
In the last twenty years many papers have appeared dealing with fuzzy theory. In particular, fuzzy integration theory had its origin in the well-known Thesis of Sugeno [7]. More recently, some authors faced this topic by means of some binary operations (see for instance [3], [8] and references): a fuzzy measure must be additive with respect to one of them, an the integral is to define in a way, which is very similar to the construction of the Lebesgue integral. On the contrary, we are interested...
Radon-Nikodym derivatives in vector integration
Radon-Nikodym property
For a Banach space and a probability space , a new proof is given that a measure , with , has RN derivative with respect to iff there is a compact or a weakly compact such that is a finite valued countably additive measure. Here we define where is a finite disjoint collection of elements from , each contained in , and satisfies . Then the result is extended to the case when is a Frechet space.
Radon-Nikodym property for vector-valued integrable functions
It is proved that if a Frechet space has property, then also has property, for .
Radon-Nikodym theorem in spaces of measures.
Radon-Nikodym type properties for Banach spaces
Ramsey, Lebesgue, and Marczewski sets and the Baire property
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on , is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is...
Random dynamics and its applications.
Random entropy and recurrence.
Random ergodic theorems for sub-Markovian operators
Random ergodic theorems with universally representative sequences
Random fractals generated by a local Gaussian process indexed by a class of functions
In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc.28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.
Random fractals generated by a local gaussian process indexed by a class of functions
In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.
Random linear functionals and random integrals
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...