Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on ?
Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on ?
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? 上多项式增长的乘法半群作用下不变的测度刚性
DOI：
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发表时间：
2008
影响因子：
0.9
通讯作者：
A. Fish
中科院分区：
文献类型：
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作者：
M. Einsiedler;A. Fish
摘要证明了圆群上的一个Borel概率测度在大的乘半群（低对数密度为正）作用下是不变的，且整个半群的作用是遍历的，则该测度要么是Lebesgue测度，要么是有限支持测度。
Abstract We prove that if a Borel probability measure on the circle group is invariant under the action of a ‘large’ multiplicative semigroup (lower logarithmic density is positive) and the action of the whole semigroup is ergodic then the measure is either Lebesgue or has finite support.