Schnorr randomness and the Lebesgue differentiation theorem
Noopur Pathak, Cristóbal Rojas, Stephen G. Simpson · Proceedings of the American Mathematical Society · 2013
We exhibit a close correspondence between $L_1$-computable functions and Schnorr tests. Using this correspondence, we prove that a point $x\in [0,1]^d$ is Schnorr random if and only if the Lebesgue Differentiation Theorem holds at $x$ for all $L_1$-computable functions $f\in L_1([0,1]^d)$.