Averaging sequences
Copyright policy )Averaging sequences
In the spirit of 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-Nikodym cocycle. Harmonic measures are examples of tangentially smooth measures for foliations and laminations. We also present sufficient hypothesis on the averaging condition under which the tangentially smooth measure is harmonic.
18 pages, minor changes, references added, final version, to appear in Pacific Journal of Mathematics
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, average condition, Means on groups, semigroups, etc.; amenable groups, Dynamical Systems (math.DS), 37A20, 43A07, 57R30, transverse invariant measure, tangentially smooth measure, lamination, FOS: Mathematics, Foliations in differential topology; geometric theory, Mathematics - Dynamical Systems, discrete equivalence relation
Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations, average condition, Means on groups, semigroups, etc.; amenable groups, Dynamical Systems (math.DS), 37A20, 43A07, 57R30, transverse invariant measure, tangentially smooth measure, lamination, FOS: Mathematics, Foliations in differential topology; geometric theory, Mathematics - Dynamical Systems, discrete equivalence relation
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