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arXiv · 1607.02644

Continuous $\times p,\times q$-invariant measures on the unit circle

Huichi Huang
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Abstract

We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational orbit. On the other hand, a continuous $\times p,\times q$-invariant measure is a continuous function on $[0,1]$ satisfying certain function equations.

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Huichi Huang. 2016-07-09. Continuous $\times p,\times q$-invariant measures on the unit circle. https://arxiv.org/abs/1607.02644

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