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Self‐Similarity and Probability: Parameters Describing the Geometry of Cantor Sets
Author(s) -
Bandt Christoph
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398005293
Subject(s) - mathematics , cantor set , similarity (geometry) , probability density function , space (punctuation) , probability measure , set (abstract data type) , probability distribution , random variable , geometry , mathematical analysis , statistical physics , discrete mathematics , statistics , artificial intelligence , linguistics , philosophy , computer science , image (mathematics) , programming language , physics
A deterministic self‐similar Cantor set F defines a natural probability space, the elements of which are neighbourhoods of various sizes of all points in F . Considering random variables on this probability space, some porosity and density parameters are explicitly calculated. 1991 Mathematics Subject Classification 28A80, 60D05.