 Let formula_1 be the set of Turing degrees of sets of natural numbers.Given some equivalence class formula_2, we may define the "cone" (or "upward cone") of formula_3 as the set of all Turing degrees formula_4 such that formula_5; that is, the set of Turing degrees which are "more complex" than formula_6 under Turing reduction.We say that a set formula_7 of Turing degrees has measure 1 under the Martin measure exactly when formula_7 contains some cone.