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<図書>
The geometry of fractal sets

責任表示 K.J. Falconer
シリーズ Cambridge tracts in mathematics ; 85
データ種別 図書
出版者 Cambridge [Cambridgeshire] ; New York : Cambridge University Press
出版年 1985
本文言語 英語
大きさ xiv, 162 p. : ill. ; 24 cm
概要 This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of...such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.
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所蔵情報


理系図1F 開架 068252190010998 414/F 13 1985

理系図3F 数理独自 068222193002953 FALC/20/1 1992

理系図3F 数理独自 068222193003016 FALC/20/1A 1992

筑紫図 自動書庫(閉架) 071232000033516 414/F 13 1985

理 物理 統計物理 068222186004667 20/F/16


数理 雑誌室 068252184011372 SER/CTM/K85A 1985

数理 雑誌室 068252186007593 SER/CTM/K85 1985
: paperback 総理工 研究室 054211996001356 413.9/F 13/54960135 1992

書誌詳細

一般注記 Bibliography: p. [150]-160
Includes index
著者標目 *Falconer, K. J., 1952-
件 名 LCSH:Fractals
LCSH:Geometric measure theory
NDLSH:変分法
分 類 LCC:QA248
DC19:515/.64
NDC8:413.9
NDC8:414
書誌ID 1000028511
ISBN 0521256941
NCID BA00234887
巻冊次 : hard covers ; ISBN:0521256941
: paperback ; ISBN:0521337054
登録日 2009.09.10
更新日 2009.09.17

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