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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

History
It was Keane who first showed that Riesz products can be regarded as strong mixing invariant measure under the shift operator S(x) = mx\, \bmod\, 1. These were later generalized by Brown and Dooley to Riesz products of the form : \prod_{k=1}^\infty \left( 1 + r_k \cos(2 \pi m_1m_2\cdots m_k t) \right) where -1 . ==References ==
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