Displaying similar documents to “Some properties of positive superharmonic functions”

Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao (1994)

Studia Mathematica

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The following results concerning boundary behavior of subharmonic functions in the unit ball of ℝ n are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the L p -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.

Choquet integrals in potential theory.

David R. Adams (1998)

Publicacions Matemàtiques

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This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions...

Some classical function theory theorems and their modern versions

J. L. Doob (1965)

Annales de l'institut Fourier

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On étudie les relations entre les valeurs d’adhérence fine en un point-frontière et les valeurs d’adhérence le long de la normale en ce point pour les fonctions sousharmoniques et les fonctions méromorphes dans un demi-plan. Des théorèmes classiques de limite à la frontière et des généralisations sont ainsi obtenues par des méthodes de théorie de potentiel. Une étude de ce genre des valeurs d’adhérence en un point singulier isolé fournit une version en topologie fine du théorème de Casorati-Weierstrass....