, Volume 5, Issue 3, pp 246-258

A unified approach to the definition of random sequences

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Abstract

Using the concept of test functions, we develop a general framework within which many recent approaches to the definition of random sequences can be described. Using this concept we give some definitions of random sequences that are narrower than those proposed in the literature. We formulate an objection to some of these concepts of randomness. Using the notion of effective test function, we formulate a thesis on the “true” concept of randomness.