G-measure
In mathematics, a G-measure is a measure that can be represented as the weak-∗ limit of a sequence of measurable functions. A classic example is the Riesz product
where. The weak-∗ limit of this product is a measure on the circle, in the sense that for :
where represents Haar measure.
History
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 formwhere.