Completeness of spaces over finitely additive probabilities
Concentration of measure and isoperimetric inequalities in product spaces
Correction to the paper "Two classes of measures''
Decomposition in the product of a measure space and a Polish space
Der "Satz von Fubini" in der allgemeinen Integrationstheorie.
Dimension of measures
Duality of measure and category in infinite-dimensional separable Hilbert space .
Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals [Book]
Ein massentheoretisches Marginalproblem.
Elliott-Morse measures and Kakutani's dichotomy theorem.
Equivalent or absolutely continuous probability measures with given marginals
Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.
Exceptional directions for Sierpiński's nonmeasurable sets
In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.
Extensions of invariant measures on Euclidean spaces
Extremal solutions of a general marginal problem
The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.
Fubini theorems for bornological measures
Homeomorphic measures on products of intervals.
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...
Infimum-convolution description of concentration properties of product probability measures, with applications
Integration by Parts
Integration seperat stetiger Funktionen