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An Embellished Account of Agafonov's Proof of Agafonov's Theorem

We give an account of Agafonov's original proof of his eponymous theorem. The original proof was only reported in Russian in a journal not widely available, and the work most commonly cited in western literature is instead the english translation of a summary version containing no proofs. The account contains some embellishments to Agafonov's original arguments, made in the interest of clarity, and provides some historical context to Agafonov's work.