Topic
Measure (mathematics)
About: Measure (mathematics) is a research topic. Over the lifetime, 23563 publications have been published within this topic receiving 417328 citations.
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Book•
27 Aug 1992
TL;DR: In this paper, the authors describe local boundary behavior in terms of curve families, curve families and capacity, and the Hausdorff measure, which is a measure of the curve families' capacity.
Abstract: 1. Some Basic Facts.- 2. Continuity and Prime Ends.- 3. Smoothness and Corners.- 4. Distortion.- 5. Quasidisks.- 6. Linear Measure.- 7. Smirnov and Lavrentiev Domains.- 8. Integral Means.- 9. Curve Families and Capacity.- 10. Hausdorff Measure.- 11. Local Boundary Behaviour.- References.- Author Index.
1,863 citations
1,707 citations
TL;DR: In this article, the authors present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entangler measures and present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entangling.
Abstract: We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures The generalization of our class of entanglement measures to more than two particles is straightforward We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement
1,443 citations
Book•
01 Jan 1994
TL;DR: In this article, the authors propose the integration of Monotone Functions on Intervals and the construction of measures using topology, based on the Radon-Nikodym Theorem.
Abstract: Preface. 1. Integration of Monotone Functions on Intervals. 2. Set Functions and Caratheodory Measurability. 3. Construction of Measures using Topology. 4. Distribution Functions, Measurability and Comonotonicity of Functions. 5. The Asymmetric Integral. 6. The Subadditivity Theorem. 7. The Symmetric Integral. 8. Sequences of Functions and Convergence Theorems. 9. Nullfunctions and the Lebesgue Spaces Lp. 10. Families of Measures and their Envelopes. 11. Densities and the Radon-Nikodym Theorem. 12. Products. 13. Representing Functionals as Integrals. References. Index.
1,327 citations
Book•
28 Apr 1995TL;DR: In this article, the Fourier transform and its application in general measure theory are discussed. But the authors focus on the analysis of general measures in the complex plane and do not address the problem of analytic capacity in complex planes.
Abstract: Acknowledgements Basic notation Introduction 1 General measure theory 2 Covering and differentiation 3 Invariant measures 4 Hausdorff measures and dimension 5 Other measures and dimensions 6 Density theorems for Hausdorff and packing measures 7 Lipschitz maps 8 Energies, capacities and subsets of finite measure 9 Orthogonal projections 10 Intersections with planes 11 Local structure of s-dimensional sets and measures 12 The Fourier transform and its applications 13 Intersections of general sets 14 Tangent measures and densities 15 Rectifiable sets and approximate tangent planes 16 Rectifiability, weak linear approximation and tangent measures 17 Rectifiability and densities 18 Rectifiability and orthogonal projections 19 Rectifiability and othogonal projections 19 Rectifiability and analytic capacity in the complex plane 20 Rectifiability and singular intervals References List of notation Index of terminology
1,262 citations