Area of isodensity contours as a measure of large-scale structure

A technique for describing quantitatively the large-scale structure of the universe is developed analytically. The isodensity contour surfaces at the nu(sigma0) level in a smoothed three-dimensional density field are associated with a statistical measure defined as the mean area of the isodensity contour per unit volume of the density field. A more easily computed function related to this measure is also derived and shown (1) to provide the same information as the genus statistic G(s) of Gott et al. (1987) and (2) to permit distinction between Gaussian and non-Gaussian distributions in the large-scale structure. 15 references