Comment (Monotone Selection) on What’s a Market Password Anyway? Towards Defining a Financial Market Random Sequence. Note Quote.

CA Stochastic

Definition:

A selection rule is a partial function r : 2 → {yes, no}.

The subsequence of a sequence A selected by a selection rule r is that with r(A|n − 1) = yes. The sequence of selected places are those ni such that r(A|ni − 1) = yes. Then for a given selection rule r and a given real A, we generate a sequence n0, n1 , . . . of selected places, and we say that a real is stochastic with respect to admissible selection rules iff for any such selection rule, either the sequence of selected places is finite, or

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