On the invariant measure for Jacobi-Perron algorithm.
On the isotropic constant of marginals
We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in , i ≤ m, then for every F in the Grassmannian , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.
On the Kluvánek Construction of the Lebesgue Integral
I. Kluvánek suggested to built the Lebesgue integral on a compact interval in the real line by the help of the length of intervals only. In the paper a modification of the Kluvánek construction is presented applicable to abstract spaces, too.
On the Kurzweil integral for functions with values in ordered spaces. II.
On the lattice group valued measures
On the lattice group valued submeasures
On the Lattice Structure of σ-Finite Measures
On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables
Let Ω be a countable infinite product of copies of the same probability space Ω₁, and let Ξₙ be the sequence of the coordinate projection functions from Ω to Ω₁. Let Ψ be a possibly nonmeasurable function from Ω₁ to ℝ, and let Xₙ(ω) = Ψ(Ξₙ(ω)). Then we can think of Xₙ as a sequence of independent but possibly nonmeasurable random variables on Ω. Let Sₙ = X₁ + ⋯ + Xₙ. By the ordinary Strong Law of Large Numbers, we almost surely have , where and E* are the lower and upper expectations. We ask...
On the lifting of invariant measures
On the local ergodic theorems of Krengel, Kubokawa, and Terrell
On the logarithmic potential defined for a Van Koch curve.
On the lower semicontinuity of certain integral functionals
Si dimostra che il funzionale è semicontinuo inferiormente su , rispetto alla topologia indotta da , qualora l’integrando sia una funzione non-negativa, misurabile in , convessa in , limitata nell’intorno dei punti del tipo , e tale che la funzione sia semicontinua inferiormente su .
On the Magnification of Cantor Sets and their Limit Models.
On the maximal run-length function in the Lüroth expansion
We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.
On the Measurability of Functions of Two Variables
On the measurability of real functions defined on product-spaces
On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space
The measurable sets of pairs of intersecting non-isotropic straight lines of type and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.
On the measurability of the conjugate and the subdifferential of a normal integrand.
On the measure of measurable sets of integers
On the measures of DiPerna and Majda
DiPerna and Majda generalized Young measures so that it is possible to describe “in the limit” oscillation as well as concentration effects of bounded sequences in -spaces. Here the complete description of all such measures is stated, showing that the “energy” put at “infinity” by concentration effects can be described in the limit basically by an arbitrary positive Radon measure. Moreover, it is shown that concentration effects are intimately related to rays (in a suitable locally convex geometry)...