What is "g-measure"

In mathematics, a G-measure is a measure μ that can be represented as the weak-∗ limit of a sequence of measurable functions G = (G). A classic example is the Riesz product

G(t) = ∏(1 + rcos(2πmt))

where $-1 < r < 1, m \in \mathbb N$. The weak-∗ limit of this product is a measure on the circle $\mathbb T$, in the sense that for $f \in C(\mathbb T)$:

∫f dμ = lim∫f(t)∏(1 + rcos(2πmt)) dt = lim∫f(t)G(t) dt

where dt represents Haar measure. The