Abstract
In this paper, we study the pointwise equidistribution properties of measures μ p defined by digit restrictions on the b-adic expansion, where b ⩾ 2 is an integer. We prove that, if a sequence satisfies a certain b-adic diversity condition, then the sequence is uniformly distributed modulo one for μ p -a.e. x. We also find some sufficient conditions to ensure the b-adic diversity. Moreover, we apply these results to establish the b-adic diversity for the sequences that can be written as certain combination of polynomial and exponential functions.
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