All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 7 Next

Displaying 121 – 140 of 290

Showing per page

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Przemysław Liszka (2014)

Open Mathematics

Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and probabilities...

The M-components of level sets of continuous functions in WBV.

Coloma Ballester, Vicent Caselles (2001)

Publicacions Matemàtiques

We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain Ω' of the image is Jordan domain, a rectangle, for instance, and...

The McShane, PU and Henstock integrals of Banach valued functions

Luisa Di Piazza, Valeria Marraffa (2002)

Czechoslovak Mathematical Journal

Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...

The mean curvature measure

Quiyi Dai, Neil S. Trudinger, Xu-Jia Wang (2012)

Journal of the European Mathematical Society

We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...

The measure algebra does not always embed

Alan Dow, Klaas Hart (2000)

Fundamenta Mathematicae

The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.

The measure extension problem for vector lattices

J. D. Maitland Wright (1971)

Annales de l'institut Fourier

Let V be a boundedly σ -complete vector lattice. If each V -valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a σ -additive measure on the generated σ -field then V is said to have the measure extension property. Various sufficient conditions on V which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: V has the...

The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals

Márcia Federson (2002)

Czechoslovak Mathematical Journal

We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, ∫ R d α ( t ) f ( t ) , where R is a compact interval of ℝ n , α and f are functions with values on L ( Z , W ) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, ∫ R α ( t ) d f ( t ) , as well as to unbounded intervals R .

The Morse minimal system is finitarily Kakutani equivalent to the binary odometer

Mrinal Kanti Roychowdhury, Daniel J. Rudolph (2008)

Fundamenta Mathematicae

Two invertible dynamical systems (X,,μ,T) and (Y,,ν,S), where X and Y are Polish spaces and Borel probability spaces and T, S are measure preserving homeomorphisms of X and Y, are said to be finitarily orbit equivalent if there exists an invertible measure preserving mapping ϕ from a subset X₀ of X of measure one onto a subset Y₀ of Y of full measure such that (1) ϕ | X ₀ is continuous in the relative topology on X₀ and ϕ - 1 | Y ₀ is continuous in the relative topology on Y₀, (2) ϕ ( O r b T ( x ) ) = O r b S ( ϕ ( x ) ) for μ-a.e. x ∈ X. (X,,μ,T) and...

Currently displaying 121 – 140 of 290