Abstract
Let u be a probability measure on 2 × 2 stochastic matrices with finite support such that the sequence μ n , the nth convolution power of μ, weakly converges to a probability measure λ whose support consists of 2 × 2 stochastic matrices with identical rows. The probability measure λ can, therefore, be regarded as a measure on the unit interval [0,1]. In this paper, we discuss some open problems regarding when λ is continuous singular or absolutely continuous with respect to the Lebesgue measure on [0,1], and when λ determines μ uniquely.
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