$p$-harmonic measure is not additive on null sets
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 2, p. 357-373
When $1 and $p\ne 2$ 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 ${E}_{1}$, ${E}_{2}$,...,${E}_{\kappa }$ in $ℝ$, of $p$-harmonic measure zero, such that ${E}_{1}\cup {E}_{2}\cup ...\cup {E}_{\kappa }\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}ℝ$.
Classification:  31A15,  35J70,  60G46
@article{ASNSP_2005_5_4_2_357_0,
author = {Llorente, Jos\'e G. and Manfredi, Juan J. and Wu, Jang-Mei},
title = {$p$-harmonic measure is not additive on null sets},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {2},
year = {2005},
pages = {357-373},
zbl = {1105.31002},
mrnumber = {2163560},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2005_5_4_2_357_0}
}

Llorente, José G.; Manfredi, Juan J.; Wu, Jang-Mei. $p$-harmonic measure is not additive on null sets. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 2, pp. 357-373. http://www.numdam.org/item/ASNSP_2005_5_4_2_357_0/

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