A generalized skew product
A generalized -porous set with a small complement.
A Geometric Theory of Surface Area.
A Geometric Theory of Surface Area.
A Geometric Theory of Surface Area. III.
A geometry on the space of probabilities (I). The finite dimensional case.
In this note we provide a natural way of defining exponential coordinates on the class of probabilities on the set Ω = [1,n] or on P = {p = (p1, ..., pn) ∈ Rn| pi > 0; Σi=1n pi = 1}. For that we have to regard P as a projective space and the exponential coordinates will be related to geodesic flows in Cn.
A geometry on the space of probabilities (II). Projective spaces and exponential families.
In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...
A Good Basis for Computing with Complex Numbers.
A group automorphism is a factor of a direct product of a zero entropy automorphism and a Bernoulli automorphism
A half-commutative IP Roth theorem.
A Horseshoe with Positive Measure.
A joint limit theorem for compactly regenerative ergodic transformations
We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.
A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications
This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.
A large set containing few orbits of measure preserving transformations.
A large set containing few orbits of measure preserving transformations. (Summary).
A Lebesgue decomposition for elements in a topological group.
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A linear Radon-Nikodym type theorem for -algebras with applications to measure theory
A local approach to -entropy
In this paper, a local approach to the concept of -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of -entropy.
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. II. Applications