A direct proof of Agafonov's theorem and an extension to shift of finite type (2005.00255v3)

Abstract: We provide a direct proof of Agafonov's theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the shift. A slightly more general statement is obtained as we show that any Markov measure is preserved by finite state compatible selection.