Weak-mixing implies sensitive dependence ✩

Let X be a metric space, B the σ -algebra of Borel subsets of X, and μ a probability measure on (X,B). In this note, for a measure-preserving map T (respectively a measure-preserving semiflow ϕ) on (X,B,μ), we prove that if suppμ = X, and T (respectively ϕ) is weak-mixing, then T (respectively ϕ) has sensitive dependence.  2004 Elsevier Inc. All rights reserved.