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We prove an Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales. Our proof is given in the framework of the game-theoretic probability of Shafer and Vovk. As many other game-theoretic proofs, our proof is self-contained and explicit.

Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach