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＜図書＞The geometry of fractal sets

責任表示 K.J. Falconer Cambridge tracts in mathematics ; 85 図書 Cambridge [Cambridgeshire] ; New York : Cambridge University Press 1985 英語 xiv, 162 p. : ill. ; 24 cm 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. 続きを見る

書誌詳細

一般注記 Bibliography: p. -160Includes index LCSH:FractalsLCSH:Geometric measure theoryNDLSH:変分法 LCC:QA248DC19:515/.64NDC8:413.9NDC8:414 1000028511 0521256941 BA00234887 : hard covers ; ISBN:0521256941: paperback ; ISBN:0521337054 2009.09.10 2009.09.17