We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

A notion of selective coideal on (FIN [∞] k ,≤) (see definitions below) is given. The natural versions of the local Ramsey property and the abstract Baire property relative to this context are proven to be equivalent, and it is also shown that the family of subsets of FIN [∞] k having the local Ramsey property relative to a selective coideal on (FIN [∞] k ,≤) is closed under the Souslin operati...

"Relative termination" is a property that generalizes both termination and "termination modulo". In order to prove that a term rewrite system relatively terminates, one may reuse the common termination quasiorderings. Further proof methods become available by the cooperation property. Relative termination sets up new proof techniques for termination and confluence. The usefulness of the notion ...

"Relative termination" is a property that generalizes both termination and "termination modulo". In order to prove that a term rewrite Systemrelatively termmates, one may reuse the common termination quasiordenngs. Further proof methods become available by the Cooperation property. Relative termination sets up new proof techniques for termination and confluence. The usefulness of the notion of ...

In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz–Thompson empirical process arising from complex sampling designs. Global such as Glivenko–Cantelli Donsker theorems, asymptotic modulus related ratio-type are proved both process, its calibrated version. Limit of other variants their conditional versions also established. Our reveals ...

In this paper we review some recent results concerning the approximations of distribution functions and measures on [0, 1] based on iterated function systems. The two different approaches available in the literature are considered and their relation are investigated in the statistical perspective. In the second part of the paper we propose a new class of estimators for the distribution function...

The Markov property of Gaussian states of CCR-algebras is studied. The detailed description is given by the representing block matrix. The proof is short and allows in nite dimension. The relation to classical Gaussian Markov triplets is also described. The minimizer of relative entropy with respect to a Gaussian Markov state has the Markov property. The appendix contains formulas for the relat...