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 |
This book studies the geometric properties of general sets and measures in euclidean space.
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 |
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 |
"'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
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 |
Modern text examining the interplay between measure theory and Fourier analysis.
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 |
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
Title | The Geometry of Fractal Sets PDF eBook |
Author | K. J. Falconer |
Publisher | Cambridge University Press |
Pages | 184 |
Release | 1985 |
Genre | Mathematics |
ISBN | 9780521337052 |
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
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 |
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.