Related papers: Absolute Continuity of Function on Topological Spa…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
We develop the general theory of \emph{topometric spaces}, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric function. Spaces of global and local types in continuous logic are the motivating examples for the…
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional…
We discuss eternal inflation in context of classical probability spaces defined by a triplet: sample space, $\sigma$-algebra and probability measure. We show that the measure problem is caused by the countable additivity axiom applied to…
Classical theorem of Luzin states that a measurable function of one real variable is "almost" continuous. For measurable functions of several variables the analogous statement (continuity on the product of sets having almost full measure)…
The present work is devoted to an extension of the well-known Ehrling inequalities, which quantitatively characterize compact embeddings of function spaces, to more general operators. Firstly, a modified notion of continuity for linear…
It is studied a connection between the separability and the countable chain condition of spaces with the $L$-property (a topological space $X$ has the $L$-property if for every topological space $Y$, separately continuous function…
We give a condition for absolute continuity of self-similar measures in arbitrary dimensions. This allows us to construct the first explicit absolutely continuous examples of inhomogeneous self-similar measures in dimension one and two. In…
Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association…
Let $\Omega \subset \mathbb{R}^{n+1}$ be an open set whose boundary may be composed of pieces of different dimensions. Assume that $\Omega$ satisfies the quantitative openness and connectedness, and there exist doubling measures $m$ on…
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise…
Two different notions of {\mu}-equicontinuity that apply to topological dynamical systems and probability measures were studied by Gilman (1987) and Huang-Lu-Ye (2011). One was used to classify measure preserving topological dynamical…
In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…