In mathematics, a G-measure is a measure that can be represented as the weak-â limit of a sequence of measurable functions . A classic example is the Riesz product
where . The weak-â limit of this product is a measure on the circle , in the sense that for :
where represents Haar measure.
It was Keane who first showed that Riesz products can be regarded as strong mixing invariant measure under the shift operator . These were later generalized by Brown and Dooley to Riesz products of the form
where .