Geodesic
On the concept of random sequence with respect
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 54-69

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This paper continues investigations on generalized probability models in which probabilities belong to fields of $p$-adic numbers. We study a $p$-adic generalization of Martin–Löf's theory based on tests for randomness. Such generalization appears to be the most natural approach to $p$-adic randomness. Each test for randomness induces a series of limit theorems. We proved that it is possible to enumerate all $p$-adic tests for randomness. However, in contrast to Martin–Löf's theory for real probabilities we proved that a universal test for randomness does not exist.
Keywords: randomness, collective, Kolmogorov model, $p$-adic numbers.
Mots-clés : von Mises model 
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     title = {On the concept of random sequence with respect},
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A. Yu. Khrennikov; Sh. Yamada. On the concept of random sequence with respect. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 54-69. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a3/