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We define a notion of finite type invariants for links with a fixed linkingmatrix. We show that Milnor's triple link homotopy invariant is a finite typeinvariant, of type 1, in this sense. We also generalize the approach toMilnor's higher order homotopy invariants and show that they are also, in asense, of finite type. Finally, we compare our approach to another approach fordefining finite type invariants within linking classes.

FINITE TYPE LINK HOMOTOPY INVARIANTS II: Milnor's $\bar\mu$-Invariants