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Uniform and Semi-uniform Convergence for Discontinuous Skew-product Transformation and Observation
In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and...
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Transportation Cost Inequalities for Stochastic Reaction-Diffusion Equations with Lévy Noises and Non-Lipschitz Reaction Terms
For stochastic reaction-diffusion equations with Lévy noises and non-Lipschitz reaction terms, we prove that W 1 H transportation cost inequalities...
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A simplified construction of the Lebesgue integral
We present a modification of Riesz’s construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time...
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Remarks on Farah’s Theorems
The aim of this paper is to prove two Farah’s Theorems concerning approximate group homomorphisms, without some assumptions present in Farah’s...
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Non-Linear Mixed Norm Spaces for Sobolev Embeddings in the Critical Case
We prove a sharp version of the endpoint Sobolev embedding in the context of non-linear function classes with mixed norms.
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Convex concentration for some additive functionals of jump stochastic differential equations
Using forward-backward stochastic calculus, we prove convex concentration inequalities for some additive functionals of the solution of stochastic...
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On multiparameter Chacon’s type ergodic theorems
The purpose of this paper is to deal with generalizations of ratio ergodic theorems due to R.V. Chacon, G. Baxter, and K. Jacobs. We prove two...
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Notes on the projective limit theorem of Kolmogorov
The new systematization in measure and integration due to the author produced a version of the Kolmogorov projective limit theorem which is far more...
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Fubini-Tonelli theorems on the basis of inner and outer premeasures
The present article obtains comprehensive Fubini-Tonelli type theorems on the basis of the author’s work in measure and integration. The basic tools...
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Projective limits via inner premeasures and the true Wiener measure
The paper continues the author’s work in measure and integration, which is an attempt at unified systematization. It establishes projective limit...
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On ordinary and standard products of infinite family of σ-finite measures and some of their applications
We introduce notions of ordinary and standard products of σ -finite measures and prove their existence. This approach allows us to construct invariant...
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Notes on the projective limit theorem of Kolmogorov
The new systematization in measure and integration due to the author produced a version of the Kolmogorov projective limit theorem which is far more...
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Product of uniform measures
For i = (1, 2), let X i be Hausdorff uniform spaces and μ i uniform measures on X i . We determine the existence of the product uniform measure μ ...
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Product of lattice-valued measures on topological spaces
X 1 and X 2 are completely regular Hausdorff spaces, E 1 , E 2 and F are Dedekind complete Banach lattices, 〈·,·〉: E 1 × E 2 → F is a bilinear...
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Upper integral and its geometric meaning
The Hahn definition of the integral is recalled, the requirement of measurability of the integrand omitted. Both the upper and lower integrals comply...
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Dependent sets of a family of relations of full measure on a probability space
For a probability space ( X, B , µ) a subfamily F of the σ -algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some...
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Affine Systems: Asymptotics at Infinity for Fractal Measures
We study measures on ℝ d which are induced by a class of infinite and recursive iterations in symbolic dynamics. Beginning with a finite set of data,...
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Statistical maps: A categorical approach
In probability theory, each random variable f can be viewed as channel through which the probability p of the original probability space is...