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Gaussian Limits for Random Measures in Geometric Probability

We establish Gaussian limits for measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general central limit theorems are applied to measures induced by random graphs (nearest neighbor, Voronoi, and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth growth models), and statistics of germ-grain models.