Vol. 255, No. 1, 2012

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Averaging sequences

Fernando Alcalde Cuesta and Ana Rechtman

Vol. 255 (2012), No. 1, 1–23

In the spirit of the Goodman–Plante average condition for the existence of a transverse invariant measure for foliations, we give an averaging condition to find tangentially smooth measures with prescribed Radon–Nikodým cocycle. Harmonic measures are examples of tangentially smooth measures for foliations and laminations. We also present a sufficient hypothesis under which the tangentially smooth measure is harmonic.

lamination, discrete equivalence relation, measure
Mathematical Subject Classification 2010
Primary: 37A20, 43A07, 57R30
Received: 8 January 2011
Revised: 26 May 2011
Accepted: 24 October 2011
Published: 14 March 2012
Fernando Alcalde Cuesta
Departamento de Xeometría e Topoloxía
Universidade de Santiago de Compostela
Rúa Lope Gómez de Marzoa s/n
15782 Santiago de Compostela
Ana Rechtman
Institut de Recherche Mathématique Avancée
Université de Strasbourg
7 rue René Descartes
67084 Strasbourg