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The basic question of this paper is: If you consider two iterated function systems close to each other in an appropriate topology, are the dimensions of their respective invariant sets close to each other? It is well known that the Hausdorff dimension (and Lebesgue measure) of the invariant set does not depend continuously on the iterated function system. Our main result is that (with a restriction on the "non-conformality" of the transformations) the Hausdorff dimension is a lower semicontinuous...

Semicontinuity of the Face-Function of a Covex Set

Victor Klee, Michael Martin (1971)

Commentarii mathematici Helvetici

Semicontinuous integrands as jointly measurable maps

Oriol Carbonell-Nicolau (2014)

Commentationes Mathematicae Universitatis Carolinae

Suppose that $(X, 𝒜)$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $𝒜^{u}$ denote the universal completion of $𝒜$ . For $x \in X$ , let $\underset{̲}{f} (x, \cdot)$ be the lower semicontinuous hull of $f (x, \cdot)$ . If $f : X \times Y \to \bar{ℝ}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable, then $\underset{̲}{f}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable.

Semi-groupes et mesures invariantes pour les processus semi-markoviens à espace d'état quelconque

Jean Jacod (1973)

Annales de l'I.H.P. Probabilités et statistiques

Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.

J. Goldstein (1976)

Semigroup forum

Semiring of Sets

Roland Coghetto (2014)

Formalized Mathematics

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.

Semiring of Sets: Examples

Roland Coghetto (2014)

Formalized Mathematics

This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].

Semisimplicity, joinings and group extensions

A. Del Junco, M. Lemańczyk, M. Mentzen (1995)

Studia Mathematica

We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].

Semivariation in $L^{p}$ -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X {\hat{\otimes}}_{τ} Y$ is their complete tensor product with respect to some tensor product topology $τ$ . A uniformly bounded $X$ -valued function need not be integrable in $X {\hat{\otimes}}_{τ} Y$ with respect to a $Y$ -valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $τ$ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index $1 \leq p < \infty$ and suppose that $X$ and $Y$ are $L^{p}$ -spaces with $τ_{p}$ the associated $L^{p}$ -tensor product...

Semivariations of an additive function on a Boolean ring

Zbigniew Lipecki (2009)

Colloquium Mathematicae

With an additive function φ from a Boolean ring A into a normed space two positive functions on A, called semivariations of φ, are associated. We characterize those functions as submeasures with some additional properties in the general case as well as in the cases where φ is bounded or exhaustive.

Separabilità di $L^{2}(\mu)$ per spazi riflessivi, $\mu$ misura gaussiana

Adriana Brogini Bratti (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Following H. Sato - Y. Okazaky we will prove that: if $X$ is a topological vector space, locally convex and reflexive, and $\mu$ is a gaussian measure on $\mathbf{C}(X,X^{\prime})$ , then $L^{2}(\mu)$ is separable.

Separating points of measures on effect algebras

Anna Avallone (2007)

Mathematica Slovaca

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

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