Search results for "Measure theory"
showing 10 items of 176 documents
Decomposable Measures and Measures of Information for Crisp and Fuzzy Sets
1983
Abstract There exist bijections between the decomposable informations of Kampe de Feriet and Forte (1967a) and the decomposable measures of Weber (1982). Using integrals for Archimedean decomposable operations, introduced by Weber (1982), informations and measures of this type are extended from crisp to fuzzy sets. For ∨-decomposable measures, Sugeno’s (1974) integral is used. For ∧-decomposable informations, Nguyen’s (1977) construction and a modification are discussed.
The Besov capacity in metric spaces
2016
We study a capacity theory based on a definition of Haj{\l} asz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are $\gamma$-medians, for which we also prove a new version of a Poincar\'e type inequality.
Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces
2006
MSC (2000) Primary: 31C35; Secondary: 31C45, 30C65 In this paper, we study the relationship between p-harmonic functions and absolutely minimizing Lipschitz extensions in the setting of a metric measure space (X, d, µ). In particular, we show that limits of p-harmonic functions (as p →∞ ) are necessarily the ∞-energy minimizers among the class of all Lipschitz functions with the same boundary data. Our research is motivated by the observation that while the p-harmonic functions in general depend on the underlying measure µ, in many cases their asymptotic limit as p →∞ turns out have a characterization that is independent of the measure. c
Closedness and lower semicontinuity of positive sesquilinear forms
2009
The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.
On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
2009
Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an absolutely summing operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.
On a multiplication and a theory of integration for belief and plausibility functions
1987
Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…
New Results on Identifiability of Nonlinear Systems
2004
Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results i…
Measuring Social Mobility
1993
Abstract The paper considers the ranking of mobility matrices in a simple Markov model of social mobility. The approach is the dynamic counterpart ot the "static" inequality ranking of income distributions by the Lorenz curve. The derived partial ordering is motivated by welfare considerations, is shown to be equivalent to same intuitive mobility concepts, and is used to screen some immobility indices. The equivalence of the ranking with the "permanent income" Lorenz ordering gives support to the claim that this approach is the natural extension of Kolm′s [The optimal production of social justice, in "Public Economics (J. Margolis and H. Guitton, Eds.), MacMillan, London, 1969], Atkinson′s …
The untranslatability of a text and the non-equivalence of words
2020
This article deals with the current state of development of two main categories of modern translation theory: “untranslatability” and “non-equivalence”. Untranslatability belongs to translation-theoretic universals and is a binary category. The essence of the phenomenon, its nature, as well as such concepts as “translation losses”, “untranslatable units”, “translatological classification of text types” are considered. The differences in the meaning of the concepts “untranslatability” and “non-equivalence” are described. The article objective is to show actuality and pecularity of their manifistation in the context of the Russian and German languages.
Passive-damping design for vibration control of large structures
2013
In this work, a systematic strategy to design passive damping systems for structural vibration control is presented. The proposed design methodology is based on the equivalence between decentralized static velocity-feedback controllers and passive damping systems. By using recent developments in static output-feedback control, the design of passivedamping systems can be formulated as a single optimization problem with Linear Matrix Inequality constraints. Moreover, this optimization problem can be efficiently solved with standard numerical tools, even for large dimension systems. Due to its computational effectiveness, the proposed methodology can be applied to the design of passive damping…