Measure-preservation and root existence of 1-Lipschitz functions on Zp in Mahler's expansion

초록

We formulate a conjecture for a measure-preservation of 1-Lipschitz functions on Zp in Mahler's expansion. In this talk we verify that it holds for a wider class of 1-Lipschitz functions that are uniformly differentiable mod p, which is a notion weaker than the usual differentiability. Furthermore we use the results obtained to provide a criterion for a root existence of 1-Lipschitz functions, which can be viewed as a generalization of Hensel’s liftting lemma.