# Definition of Mean Squared Value Error with respect to action-value functions in Reinforcement Learning algorithms

I am referring to page 199 of Sutton and Barto book on Reinforcement Learning available here: book

There the Mean Squared Value Error for an vector-parameterized function approximation $$\hat{v}(s,\mathbf{w})$$ of the true value function of a given policy $$\pi$$ is defined as

$$\overline{VE}(\mathbf{w}) \equiv \sum_{s \in \mathcal{S}} \mu (s)\left[v_{\pi}(s)- \hat{v}(s,\mathbf{w})\right]^2$$

where $$\mu(s)$$ is some distribution ($$\mu(s) \geq 0, \sum_s \mu(s) =1$$) over $$\mathcal{S}$$.

What would be its definition with respect to action-value approximation functions $$\hat{q}(s,a,\mathbf{w})$$? Is it correct, by recalling that $$v_{\pi}(s)= \sum_a \pi(a|s)q_{\pi}(s,a)$$, to define it as

$$\overline{VE}(\mathbf{w}) \equiv \sum_{s \in \mathcal{S}} \mu (s) \sum_{a \in \mathcal{A}(s)} \pi(a|s)\left[q_{\pi}(s,a)- \hat{q}(s,a,\mathbf{w})\right]^2$$