Non-Borel measures on non-separable metric spaces
Non-Hilbertian structure of the Wiener measure
Nonlinear structures determined by measures on Banach spaces
Noyaux multiplicatifs d'un processus de Markov
Numerical solutions of the mass transfer problem
Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost ∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval. We illustrate these numerical...
Obata’s Rigidity Theorem for Metric Measure Spaces
We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.
On a characterization of gaussian measures in a Hilbert space
On a characterization theorem on finite Abelian groups.
On a class of covariance operators.
On a Theorem of Wald and Wolfowitz on Randomization in Statistics.
On analytical properties of generalized convolutions
The paper is, for the most part, devoted to a survey of the analytical properties of generalized convolution algebras and their realizations. This issue appears to be the state of the art until now because intensive research on the generalized convolution and the related models still persists.
On Banach spaces containing . A supplement to the paper by J.Hoffman-Jørgensen “Sums of independent Banach space valued random variables”
On conditional expectations of vector valued variables
On Hausdorff dimension of random fractals.
On heredity of strongly proximal actions
We prove that action of a semigroup on compact metric space by continuous selfmaps is strongly proximal if and only if action on is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
On infinite products of independent random elements on metric semigroups
On Kakutani's Dichotomy Theorem for Infinitive Products of not Necessarily Independent Functions.
On Prohorov spaces
On Skorohod embedding in -dimensional brownian motion by means of natural stopping times
On some definition of expectation of random element in metric space
We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.