MPEJ Volume 10, No. 4, 12 pp.
Received: Nov 4, 2003. Revised: Mar 3, 2004. Accepted: Mar 18, 2004.

G. Androulakis, S. Dostoglou
Space Averages and Homogeneous Fluid Flows

ABSTRACT: The relation between space averages of vector fields in
$L^1_{\text{loc}}(\mathbb{R}^3)$ and averages with respect to
homogeneous measures on such vector fields is examined. The space
average, obtained by integration over balls in space, is shown to
exist almost always and, whenever the measure is ergodic or the
correlation decays, to equal the ensemble average.


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