On a class of singular measures satisfying a strong annular decay condition

Abstract

A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we construct examples of singular measures it on RN such that (RN,d, t) satisfies the strong annular decay condition.