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. http://www.maia.ub.es/mpej/Vol/10/4.ps http://www.maia.ub.es/mpej/Vol/10/4.pdf http://www.ma.utexas.edu/mpej/Vol/10/4.ps http://www.ma.utexas.edu/mpej/Vol/10/4.pdf http://mpej.unige.ch/mpej/Vol/10/4.ps http://mpej.unige.ch/mpej/Vol/10/4.pdf