Bulletin of the London Mathematical Society · 2006 · 44 citations · 17 references
Natural SciencesMathematicsPhysicsMathematical PhysicsProbability TheorySet TheoryCritical PhenomenaMeasure-theoretic ProbabilityRegular SolutionsSingularity Measures
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).
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Composite Media and Asymptotic Dirichlet Forms
U. Mosco · Journal of Functional Analysis · 1994 · 341 citations
Harmonic calculus on p.c.f.\ self-similar sets
Jun Kigami · Transactions of the American Mathematical Society · 1993 · 329 citations · Full text
Brownian motion on nested fractals
Tom Lindstrøm · Memoirs of the American Mathematical Society · 1990 · 325 citations · Full text