Let $X$ be a vector space and let $\phi, \psi \in X^\ast$ be two linear forms on $X.$ It is well known that if, for any $x \in X, $

$$\phi(x) = 0 \Rightarrow \psi(x) = 0,$$

then $\psi = c \phi$ for some scalar $c.$ A continuous version is also known. Namely, if $X$ has a norm, if $||\phi|| = \| \psi \| = 1,$ and if, for any $x \in X,$ with $ \|x\| = 1,$

$$\phi(x) = 0 \Rightarrow |\psi(x)| < \epsilon,$$

then either $||\phi + \psi|| < 2\epsilon$ or $||\phi - \psi|| < 2\epsilon.$

In this talk, we will discuss analogous questions for the case of multilinear forms on a product of spaces, $X_1 \times \cdots \times X_n \to \mathbb{K}.$

(This is joint work with A Cardwell, L. Downey, D. García, M. Maestre, and I. Zalduendo.)