This presentation explores consequences of the relationship between two concepts that have been found useful in recent work on convolution algebras. A uniform measure on a uniform space is a linear functional on the space of bounded uniformly continuous functions that is pointwise continuous on every uniformly equicontinuous set of functions. In some sense uniform measures are an appropriate substitute for finite Radon measures as we move from complete metric spaces or locally compact groups to more general spaces. Using the language of topological dynamics, ambitability formalizes a certain factorization property in function spaces on (semi)groups. It is an open problem whether every topological group is either precompact or ambitable. However, the answer is positive for “most” topological groups, including all locally compact and all ℵn-bounded groups, n = 1, 2,... . Along with general properties of uniform measures, this yields some known and some new results, including those about uniquely amenable groups and about Radon measures on locally compact groups in duality with bounded uniformly continuous functions.