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

Llorente, José G.; Manfredi, Juan J.; Wu, Jang-Mei

Geodesic

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-harmonic measure is not additive on null sets

Llorente, José G.¹ ; Manfredi, Juan J.² ; Wu, Jang-Mei ³

¹ Department de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra, Spain
² Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, USA
³ Department of Mathematics University of Illinois 1409 West Green Street Urbana, IL 61801, USA

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 2, pp. 357-373

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Résumé

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 $E_{1} \cup E_{2} \cup . . . \cup E_{κ} = ℝ$ .

MR Zbl

Classification : 31A15, 35J70, 60G46

Affiliations des auteurs :

Llorente, José G. ¹ ; Manfredi, Juan J. ² ; Wu, Jang-Mei ³

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     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},
     pages = {357--373},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {2},
     year = {2005},
     mrnumber = {2163560},
     zbl = {1105.31002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_2_357_0/}
}

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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://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_2_357_0/