 The following subsections make precise the notions invoked in the definition and show "f"("T") is indeed well defined under given assumptions.For a continuous function "g" defined in an open neighborhood of Γ and taking values in "L"("X"), the contour integral ∫Γ"g" is defined in the same way as for the scalar case.One can parametrize each γ"i" ∈ Γ by a real interval ["a", "b"], and the integral is the limit of the Riemann sums obtained from ever-finer partitions of ["a", "b"].