(Hens \& Rieger [938], Corollary 2.31) Suppose that the expected utility function \(\mathbb{E}[u(\tilde{x})]\) of a risk averse agent can be represented through a continuous mean-variance function \(V\left(\mathbb{E}[\tilde{x}], \sigma^{2}(\tilde{x})\right)\), strictly increasing in the first argument, for any \(\sigma^{2}(\tilde{x})\). Then the preference relation represented by \(\mathbb{E}[u(\tilde{x})]\) does not satisfy the independence axiom.