Tensor Derivations

Define (\mathcal{D}_\mathcal{U}B)_p = \mathcal{D}(fB)_p. This is well defined since if g is another bump function then

\mathcal{D}(fgB)_p = \mathcal{D}(f)_p(gB)(p) + f(p)\mathcal{D}(gB)_p = \mathcal{D}(gB)_p

and reversing f and g gives

\mathcal{D}(gfB)_p = \mathcal{D}(g)_p(fB)(p) + g(p)\mathcal{D}(fB)_p = \mathcal{D}(fB)_p

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