Search results for "Riesz–Markov–Kakutani representation theorem"

showing 5 items of 5 documents

A space on which diameter-type packing measure is not Borel regular

1999

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.

CombinatoricsBorel equivalence relationRiesz–Markov–Kakutani representation theoremApplied MathematicsGeneral MathematicsRadon measureStandard probability spaceBaire measureBorel setBorel measureMeasure (mathematics)MathematicsProceedings of the American Mathematical Society
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On the structure of the ultradistributions of Beurling type

2008

Let O be a nonempty open set of the k-dimensional euclidean space Rk. In this paper, we give a structure theorem on the ultradistributions of Beurling type in O. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in O.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsAlgebra and Number TheoryEuclidean spaceRiesz–Markov–Kakutani representation theoremApplied MathematicsOpen setStructure (category theory)Banach spaceType (model theory)Computational MathematicsLocally convex topological vector spaceGeometry and TopologyAnalysisStructured program theoremMathematicsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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Hausdorff measures, Hölder continuous maps and self-similar fractals

1993

Let f: A → ℝn be Hölder continuous with exponent α, 0 < α ≼ 1, where A ⊂ ℝm has finite m-dimensional Lebesgue measure. Then, as is easy to see and well-known, the s-dimensional Hausdorif measure HS(fA) is finite for s = m/α. Many fractal-type sets fA also have positive Hs measure. This is so for example if m = 1 and f is a natural parametrization of the Koch snow flake curve in ℝ2. Then s = log 4/log 3 and α = log 3/log 4. In this paper we study the question of what s-dimensional sets in can intersect some image fA in a set of positive Hs measure where A ⊂ ℝm and f: A → ℝn is (m/s)-Hölder continuous. In Theorem 3·3 we give a general density result for such Holder surfacesfA which implies…

CombinatoricsLebesgue measureRiesz–Markov–Kakutani representation theoremGeneral MathematicsTotally disconnected spaceHausdorff dimensionMathematical analysisOuter measureAlmost everywhereHausdorff measureMeasure (mathematics)MathematicsMathematical Proceedings of the Cambridge Philosophical Society
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A Note on Locally ??-compact Spaces

1995

: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.

Class (set theory)Pure mathematicsRiesz–Markov–Kakutani representation theoremGeneral NeuroscienceVague topologyHausdorff spaceMathematics::General TopologyLocally compact groupContinuous functions on a compact Hausdorff spaceGeneral Biochemistry Genetics and Molecular BiologyCompact spaceHistory and Philosophy of ScienceRelatively compact subspaceMathematicsAnnals of the New York Academy of Sciences
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Equivalence Relations on Stonian Spaces

1996

Abstract Quotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved.

Mathematics(all)Representation theoremquotient spaceRiesz–Markov–Kakutani representation theoremGeneral Mathematicsba spacerepresentation of a space of measuresQuotient space (linear algebra)Stone representation spaceAlgebranormal Radon measureStonian spaceEquivalence relationLocally compact spaceStone's representation theorem for Boolean algebrasQuotientfinitely additive measureMathematicsAdvances in Mathematics
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