Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...

Let µ be a probability measure on the real line with finite moments of all orders. Apply the Gram-Schmidt orthogonalization process to the system {1, x, x², . . . , xn, . . .} to get orthogonal ...