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p -harmonic measure is not additive on null sets

José G. Llorente, Juan J. Manfredi, Jang-Mei Wu (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

When 1 < p < and p 2 the p -harmonic measure on the boundary of the half plane + 2 is not additive on null sets. In fact, there are finitely many sets E 1 , E 2 ,..., E κ in , of p -harmonic measure zero, such that E 1 E 2 . . . E κ = .

Plurisubharmonic martingales and barriers in complex quasi-Banach spaces

Nassif Ghoussoub, Bernard Maurey (1989)

Annales de l'institut Fourier

We describe the geometrical structure on a complex quasi-Banach space X that is necessay and sufficient for the existence of boundary limits for bounded, X -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...

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