p-Harmonic measure is not additive on null sets
نویسندگان
چکیده
منابع مشابه
p-HARMONIC MEASURE IS NOT SUBADDITIVE
When 1 < p < ∞ and p 6= 2 the p-harmonic measure on the boundary of the half plane R+ is not subadditive. In fact, there are finitely many sets E1, E2,...,Eκ on R, of p-harmonic measure zero, such that E1 ∪ E2 ∪ ... ∪ Eκ = R.
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§1. The basic definitions and the main theorem. 1. Definition. (1) We define addition on 2 as addition modulo 2 on each component, i.e., if x, y, z ∈ 2 and x+ y = z then for every n we have z(n) = x(n) + y(n) (mod 2). (2) For A,B ⊆ 2 and x ∈ 2 we set x + A = {x + y : y ∈ A}, and we define A + B similarly. (3) We denote the Lebesgue measure on 2 with μ. We say that X ⊆ 2 is null-additive if for ...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2009
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.2005.2.06