Characterization of Kurtz Randomness by a Differentiation Theorem

Brattka, Miller and Nies (2012) showed that some major algorithmic randomness notions are characterized via differentiability. The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space. The proof shows that integral tests play an essential part and shows that how randomness and differentiation are connected.

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