Imbedding theorems for spaces of functions of a denumberable number of variables and their applications.
Implicit Markov kernels in probability theory
Having Polish spaces , and we shall discuss the existence of an -valued random vector such that its conditional distributions satisfy or for some maps , or multifunction respectively. The problem is equivalent to the existence of universally measurable Markov kernel defined implicitly by or respectively. In the paper we shall provide sufficient conditions for the existence of the desired Markov kernel. We shall discuss some special solutions of the - or -problem and illustrate...
Independent families on complete Boolean algebras
Individual ergodic theorem in a regular space
Individual ergodic theorem on a logic
Induced and amenable ergodic actions of Lie groups
Induced contraction semigroups and random ergodic theorems [Book]
Induced ...-Homomorphisms and a Parametrization of Measurable Sections via Extremal Preimage Measures.
Induced measures on Wallman spaces.
Induzierte Maße bei Lürothschen Reihen.
Inégalités isopérimétriques en analyse et probabilités
Inequalities for product operators and vector valued ergodic theorems
Inequalities for the ergodic maximal function
Infimum-convolution description of concentration properties of product probability measures, with applications
Infinite combinatorics in Function spaces: Category methods
Infinite ergodic index -actions in infinite measure
We construct infinite measure preserving and nonsingular rank one -actions. The first example is ergodic infinite measure preserving but with nonergodic, infinite conservative index, basis transformations; in this case we exhibit sets of increasing finite and infinite measure which are properly exhaustive and weakly wandering. The next examples are staircase rank one infinite measure preserving -actions; for these we show that the individual basis transformations have conservative ergodic Cartesian...
Infinite invariant measures for non-uniformely expanding transformations of [0, 1]: weak law of large numbers with anamalous scaling.
Infinite Iterated Function Systems: A Multivalued Approach
We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.
Infinitely divisible cylindrical measures on Banach spaces
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on...
Information measures and uncertainty of particular symbols
The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced...