Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 40 for “"measure theory"”.
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Nonstandard Models in Measure Theory and in functional Analysis
… with the study of nonstandard models in measure theory and in functional analysis. In measure theory, we define elementary numerosities, that are additive measures that take on values in a non-archimedean field and for which the measure of every singleton is 1. We have shown that, by …
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A Little Aspect of Real Analysis, Topology and Probability
… <p><strong>Part two</strong>: demonstrate the measure and probability which is one of the main topics in this work. This section serves as an introduction for the remaining part. It explains the construction of the σ-algebra and the Borel set, and the usefulness of the Borel set in the …
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Weak Radon-Nikdoym Sets in Dual Banach Spaces
The interplay between geometry, topology, measure theory and operator theory has long been evident in the study of the Radon-Nikodym property. Recently results of substantial interest in the structure of Banach spaces have been obtained by localizing these ideas to individual subsets. The study of …
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Representation of measures via the standard part map
… we study the representation of standard measures and contents via Loeb measures and the standard part map, extending previously known results to a nontopological setting. In addition, a characterization of the completely regular and Hausdorff spaces which are universally Loeb measurable …
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Uma formalização da mecânica clássica dos corpos rígidos
… Only elementary concepts of bilinear algebra and measure theory are used. We restrict ourselves to the problems of the determination of the required forces to produce and sustain any well-behaved motion of a given rigid body and then suggest a interpretation for the resolution. of the reciprocal …
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Equivalent norms on L[superscript p] and E[superscript p] (T) speces
In this paper we will be considering two measures on sorae measure space (X, A). For general p > o we can consider the tiro norms |jf|[p,y and }|fj|p,v. We are interested in conditions on y and v that make ||f||p, y - | [f | |p,v for all f in sorae class of functions, i.e. when there exist positive …
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Distance Sets and Gap Lemma
Many problems in geometric measure theory are centered around finding conditions and structures on a set to guarantee that its distance set must be large. Two notions of structure that are of importance in this work are Hausdorff dimension and thickness. Recent progress has been made on …
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Contributions to spatial uncertainty modelling in GIS : small sample data
… as geostatistics, fuzzy mathematics Grey System Theory, and (V,·) Credibility Measure Theory. Fifteen papers including three journal papers were written in contribution to the developments of spatial fuzzy and grey uncertainty modelling, in which I have a contributed portion of 50 to 65%. The …
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Synthesis of insightful algorithms
… the environmental observations and the sensors measurements, to membership functions representing the expectations of the system's models. This couples Probability Theory to Fuzzy Set Theory, and uses Zadeh's concept of the probability of a Fuzzy event. Estimation of the future performance level …
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Detection of non-coding RNA with comparative genomics and the sequential closure of smooth graphs in Cartesian currents
… cDNA for ncRNA genes. In the field of geometric measure theory, it proves that the set of cartesian currents given by integration over the graphs of smooth functions is dense in the set of all cartesian currents.
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Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications
In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space through studying a class of sets S which approximates A well in small balls. We …
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An Introduction to the Lebesgue Integral
… of the Lebesgue integral requires the use of measure theory since picking out a suitable class of measurable subsets is an essential prerequisite for Lebesgue integral. The central concepts in this paper are Lebesgue measure and the Lebesgue integral. Examples as well as theorems and proofs …
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The Mattila-Sjölin Problem for Triangles
… problem which establishes a positive Lebesgue measure for the distance set instead of it having nonempty interior
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A Contribution to Metric Diophantine Approximation : the Lebesgue and Hausdorff Theories
This thesis is concerned with the theory of Diophantine approximation from the point of view of measure theory. After the prolegomena which conclude with a number of conjectures set to understand better the distribution of rational points on algebraic planar curves, Chapter 1 provides an extension …
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Mathematical Connections between Convolutional Neural Networks and the Scattering Transformation
… construction of wavelets and basic principles of measure theory, which are used in both the scattering and the windowed scattering. Next, we review extensions of this theory: representing the scattering transformation on a stochastic process, ensuring the scattering works over …
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A Mass Minimizing Flow for Real-Valued Flat Chains with Applications to Transport Networks
An oriented transportation network can be modeled by a 1-dimensional chain whose boundary is the difference between the demand and supply distributions, represented by weighted sums of point masses. To accommodate efficiencies of scale into the model, one uses a suitable Mα norm for transportation …
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Local Criteria in Polyhedral Minimizing Problems
This thesis will discuss two polyhedral minimizing problems and the necessary local criteria we find any such minimizers must have. We will also briefly discuss an extension of a third minimizing problem to higher dimension. The first result we present classifies the three-dimensional piecewise …
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TOWARDS DATA DRIVEN NETWORK EPIDEMIC MODELING.
… to make contributions on both fronts and span theory and applications. Our contributions to the estimation of the epidemic networks are twofold. First, we propose a theoretical result combining measure theory and spectral graph theory to produce estimates of the spectral radius of a network …
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Hausdorff Dimension of Wildly Embedded Zero Dimensional Subspaces of R³
No abstract prepared.
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