Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In descriptive set theory, the Martin measure is a filter on the set of Turing degrees of sets of natural numbers. Under the axiom of determinacy it can be shown to be an ultrafilter. Let D be the set of Turing degrees of sets of natural numbers. Given some equivalence class [X]in D, we may define the cone (or upward cone) of [X] as the set of all Turing degrees [Y] such that Xle_T Y; that is, the set of Turing degrees which are "more complex" than X under Turing reduction.

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