Geometry of Sets and Measures in Euclidean Spaces PDF Download

Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 9780521655958
Category : Mathematics
Languages : en
Pages : 360

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

Author: Pertti Mattila
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: Frank Jones
Publisher: Jones & Bartlett Learning
ISBN: 9780763717087
Category : Computers
Languages : en
Pages : 626

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Book Description
"'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" --

Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 1009288083
Category : Mathematics
Languages : en
Pages : 181

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Book Description
A broad survey of the theory of rectifiability and its deep connections to numerous different areas of mathematics.

Author: Jan Rataj
Publisher: Springer
ISBN: 3030181839
Category : Mathematics
Languages : en
Pages : 256

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Book Description
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.

Author: Herbert Federer
Publisher: Springer
ISBN: 3642620108
Category : Mathematics
Languages : en
Pages : 694

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Book Description
"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)

Author: K. J. Falconer
Publisher: Cambridge University Press
ISBN: 9780521337052
Category : Mathematics
Languages : en
Pages : 184

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Book Description
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.

Author: Francesco Maggi
Publisher:
ISBN: 9781107471726
Category :
Languages : en
Pages : 454

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Book Description

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646795
Category : Mathematics
Languages : en
Pages : 344

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Book Description
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Author: Pertti Mattila
Publisher: Cambridge University Press
ISBN: 1107107350
Category : Mathematics
Languages : en
Pages : 455

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