Consider the following text from Folland's text "Real analysis":
In theorem 1.15, I'm a bit confused: How is $\mu_0$ defined on sets of the form $(a, \infty)$? Don't we need to say how $\mu_0$ is defined on sets of that form? I.e. it seems $\mu_0$ is not defined on all of $\mathcal{A}$.