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- In exterior algebra: Suppose that v1, ..., vp are linearly independent elements of a vector space V and w1, ..., wp are such that
- in ΛV. Then there are scalars hij = hji such that
- In several complex variables: Let a1 < a2 < a3 < a4 and b1 < b2 and define rectangles in the complex plane C by
- so that . Let K2, ..., Kn be simply connected domains in C and let
- so that again . Suppose that F(z) is a complex analytic matrix-valued function on a rectangle K in Cn such that F(z) is an invertible matrix for each z in K. Then there exist analytic functions in and in such that
- in K.
- In potential theory, a result that estimates the Hausdorff measure of the set on which a logarithmic Newtonian potential is small. See Cartan's lemma (potential theory).