We investigate the dense and sparse regions of a d-dimensional Poisson process and establish strong laws for both the maximal and the minimal number of points in families of sets of a certain volume.

Diaconis and Ylvisaker (1979) give necessary conditions for conjugate priors for distributions from the natural exponential family to be proper as well as to have the property of linear posterior expectation of the mean parameter of the family. Their conditions for propriety and linear posterior...