On the concept of a random sequence

Abstract

Von Mises has based his frequency theory of probability on the notion of a Kollektiv, 2 that is, of an infinite sequence of trials of an event whose possible outcomes have each a definite probability but otherwise appear entirely at random. (Convenient illustrative examples are an infinite sequence of tosses of a coin, an infinite sequence of rolls of a die, and the like.) 3 Abstractly the Kollektiv may be represented by an infinite sequence of points of an appropriate space, the Merkmalraum. Or if the number of possible outcomes of a trial is finite (and it may well be argued that this is always the case for any actual physical observation 4 ), it is sufficient to employ an infinite sequence of natural numbers which are less than a fixed natural number. This infinite sequence-of points or of natural numbers-satisfies certain conditions which correspond to those appearing in the description of a Kollektiv as just given, and which we shall express by saying that it is a random sequence (regellose Folge).