Geometry of Sets and Measures in Euclidean Spaces

Geometry of Sets and Measures in Euclidean Spaces
Title Geometry of Sets and Measures in Euclidean Spaces PDF eBook
Author Pertti Mattila
Publisher Cambridge University Press
Pages 360
Release 1999-02-25
Genre Mathematics
ISBN 9780521655958

Download Geometry of Sets and Measures in Euclidean Spaces Book in PDF, Epub and Kindle

This book studies the geometric properties of general sets and measures in euclidean space.

Geometry of sets and measures in euclidean spaces

Geometry of sets and measures in euclidean spaces
Title Geometry of sets and measures in euclidean spaces PDF eBook
Author Pertti Mattila
Publisher
Pages
Release 1992
Genre
ISBN

Download Geometry of sets and measures in euclidean spaces Book in PDF, Epub and Kindle

Lebesgue Integration on Euclidean Space

Lebesgue Integration on Euclidean Space
Title Lebesgue Integration on Euclidean Space PDF eBook
Author Frank Jones
Publisher Jones & Bartlett Learning
Pages 626
Release 2001
Genre Computers
ISBN 9780763717087

Download Lebesgue Integration on Euclidean Space Book in PDF, Epub and Kindle

"'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --

Fourier Analysis and Hausdorff Dimension

Fourier Analysis and Hausdorff Dimension
Title Fourier Analysis and Hausdorff Dimension PDF eBook
Author Pertti Mattila
Publisher Cambridge University Press
Pages 455
Release 2015-07-22
Genre Mathematics
ISBN 1107107350

Download Fourier Analysis and Hausdorff Dimension Book in PDF, Epub and Kindle

Modern text examining the interplay between measure theory and Fourier analysis.

Curvature Measures of Singular Sets

Curvature Measures of Singular Sets
Title Curvature Measures of Singular Sets PDF eBook
Author Jan Rataj
Publisher Springer
Pages 256
Release 2019-06-22
Genre Mathematics
ISBN 3030181839

Download Curvature Measures of Singular Sets Book in PDF, Epub and Kindle

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.

The Geometry of Fractal Sets

The Geometry of Fractal Sets
Title The Geometry of Fractal Sets PDF eBook
Author K. J. Falconer
Publisher Cambridge University Press
Pages 184
Release 1985
Genre Mathematics
ISBN 9780521337052

Download The Geometry of Fractal Sets Book in PDF, Epub and Kindle

A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.

Sets of Finite Perimeter and Geometric Variational Problems

Sets of Finite Perimeter and Geometric Variational Problems
Title Sets of Finite Perimeter and Geometric Variational Problems PDF eBook
Author Francesco Maggi
Publisher Cambridge University Press
Pages 475
Release 2012-08-09
Genre Mathematics
ISBN 1139560891

Download Sets of Finite Perimeter and Geometric Variational Problems Book in PDF, Epub and Kindle

The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.