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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 $1 < p < \infty$ and $p \neq 2$ the $p$ -harmonic measure on the boundary of the half plane $ℝ_{+}^{2}$ is not additive on null sets. In fact, there are finitely many sets $E_{1}$ , $E_{2}$ ,..., $E_{κ}$ in $ℝ$ , of $p$ -harmonic measure zero, such that $E_{1} \cup E_{2} \cup . . . \cup E_{κ} = ℝ$ .

Nonlinear harmonic measures on trees.

Kaufman, Robert; Llorente, José G.; Wu, Jang-Mei — 2003

Annales Academiae Scientiarum Fennicae. Mathematica

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p -harmonic measure is not additive on null sets

Nonlinear harmonic measures on trees.

$p$ -harmonic measure is not additive on null sets