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Banach spaces --- Banach spaces --- Convexity spaces --- Radon-Nikodym property

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This paper presents axiomatic arguments to make the case for distribution-sensitive multidimensional poverty measures. The commonly-used counting measures violate the strong transfer axiom which requires regressive transfers to be unambiguously poverty-increasing and they are also invariant to changes in the distribution of a given set of deprivations amongst the poor. The paper appeals to strong transfer as well as an additional cross-dimensional convexity property to offer axiomatic justification for distribution-sensitive multidimensional poverty measures. Given the nonlinear structure of these measures, it is al also shown how the problem of an exact dimensional decomposition can be solved using Shapley decomposition methods to assess dimensional contributions to poverty. An empirical illustration for India highlights distinctive features of the distribution-sensitive measures.

Crossdimensional Convexity --- Multidimensional Poverty --- Poverty Assessment --- Poverty Measurement --- Poverty Reduction --- Shapley Decomposition --- Transfer Axiom

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Integral geometry --- Convex domains --- Convex regions --- Convexity --- Calculus of variations --- Convex geometry --- Point set theory --- Geometry, Integral --- Geometry, Differential

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Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biolo

Convex domains --- Geometry --- -Mathematics --- Euclid's Elements --- Convex regions --- Convexity --- Calculus of variations --- Convex geometry --- Point set theory --- Data processing --- Convex domains. --- Data processing. --- -Data processing

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Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Convex domains. --- Mechanics, Applied -- Mathematical models. --- Mechanics, Applied --- Convex domains --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Mathematical models --- Mathematical models. --- Convex regions --- Convexity --- Engineering. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Calculus of variations --- Convex geometry --- Point set theory --- Mechanics, applied. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Rank-one convexity