Proposition 1.2.10 in "Cohen-Macaulay Rings" by W. Bruns, H.J. Herzog: if $R$ is a Noetherian ring, $I$ an ideal of $R$, and $M$ a finite $R$-module, then $$\operatorname{grade} (I,M)= \inf \{\operatorname{depth} M_p | p \in V(I)\}.$$
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