LIPSCHITZIAN ELEMENTS OVER p-ADIC FIELDS

Let p be a prime number, Qp the field of p-adic numbers, K a finite field extension of Qp, skew4 bar K a fixed algebraic closure of K, and Cp the completion of skew4 bar K with respect to the p-adic valuation. We discuss some properties of Lipschitzian elements, which are elements T of Cp defined by a certain metric condition that allows one to integrate Lipschitzian functions along the Galois orbit of T over K with respect to the Haar distribution.