F. Alcalde Cuesta, A. Rechtman. Averaging sequences. Pacific Journal of Mathematics 255 (2012), 1-23.

DOI: 10.2140/pjm.2012.255.1

Abstract. 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 a prescribed Radon-Nikodym cocycle. Harmonic measures are examples of tangentially smooth measures for foliations and laminations. We also present a sufficient hypothesis on the averaging condition under which the tangentially smooth measure is harmonic.