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On Singularity of Energy Measures on Self‐Similar Sets II
Author(s) -
Hino Masanori,
Nakahara Kenji
Publication year - 2006
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/s0024609306019072
Subject(s) - mathematics , singularity , mathematics subject classification , measure (data warehouse) , dirichlet distribution , interpretation (philosophy) , probabilistic logic , pure mathematics , energy (signal processing) , mathematical analysis , statistics , data mining , computer science , programming language , boundary value problem
We provide a criterion for the energy measures of regular Dirichlet forms on post‐critically finite self‐similar sets to be singular with respect to every self‐similar measure. A probabilistic interpretation of the singularity is also discussed. 2000 Mathematics Subject Classification 60G30 (primary), 28A80, 31C25, 60J60 (secondary).