Geometry Of Sets And Measures In Euclidean Spaces
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Geometry Of Sets And Measures In Euclidean Spaces
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-25
Geometry Of Sets And Measures In Euclidean Spaces written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-25 with Mathematics categories.
This book studies the geometric properties of general sets and measures in euclidean space.
Geometry Of Sets And Measures In Euclidean Spaces
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Author : Pertti Mattila
language : en
Publisher:
Release Date : 1992
Geometry Of Sets And Measures In Euclidean Spaces written by Pertti Mattila and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Rectifiability
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-12
Rectifiability written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-12 with Mathematics categories.
A broad survey of the theory of rectifiability and its deep connections to numerous different areas of mathematics.
Curvature Measures Of Singular Sets
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Author : Jan Rataj
language : en
Publisher: Springer
Release Date : 2019-06-22
Curvature Measures Of Singular Sets written by Jan Rataj and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-22 with Mathematics categories.
The book describes how curvature measures can be introduced for certain classes of sets with singularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.
Fourier Analysis And Hausdorff Dimension
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-22
Fourier Analysis And Hausdorff Dimension written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Modern text examining the interplay between measure theory and Fourier analysis.
Sets Of Finite Perimeter And Geometric Variational Problems
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Author : Francesco Maggi
language : en
Publisher:
Release Date : 2012
Sets Of Finite Perimeter And Geometric Variational Problems written by Francesco Maggi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Rectifiable Sets Densities And Tangent Measures
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Author : Camillo De Lellis
language : en
Publisher: European Mathematical Society
Release Date : 2008
Rectifiable Sets Densities And Tangent Measures written by Camillo De Lellis and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Analysis In Euclidean Space
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Author : Kenneth Hoffman
language : en
Publisher: Courier Dover Publications
Release Date : 2019-07-17
Analysis In Euclidean Space written by Kenneth Hoffman and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-17 with Mathematics categories.
Developed for an introductory course in mathematical analysis at MIT, this text focuses on concepts, principles, and methods. Its introductions to real and complex analysis are closely formulated, and they constitute a natural introduction to complex function theory. Starting with an overview of the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings addresses implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a Bibliography, List of Symbols, Index, and an Appendix with background in elementary set theory.
Problems In Euclidean Space
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Author : Harold Gordon Eggleston
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Problems In Euclidean Space written by Harold Gordon Eggleston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of two or three dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. Problems in Euclidean Space features four chapters that develop an increasingly dominant influence of convexity. In the first chapter, convexity plays a minor role; the second chapter considers problems originally stated in a wider context that can be reduced to problems concerning convex sets. In the third chapter, the problems are defined strictly for convex sets and not for more general sets, and the final chapter discusses properties of subclasses of the class of convex sets.
Lebesgue Integration On Euclidean Space
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Author : Frank Jones
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 1993
Lebesgue Integration On Euclidean Space written by Frank Jones and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The treatment of integration developed by Henri Lebesgue almost a century ago rendered previous theories obsolete and has yet to be replaced by a better one. The author presents an extended introduction to Lebesgue integration, deals with n-dimensional space from the outset, and provides a thorough treatment of Fourier analysis. Other topics include Lebesgue measure, invariance, Cantor sets, algebras of sets and measurable functions, the gamma function, convolutions, and products of abstract measures. Many exercises are incorporated with the text. Annotation copyright by Book News, Inc., Portland, OR