Name of a particular kind of measures

Question

Is there any particular name given to measures $\mu$ for which there exists $g\in\mathbb{L}^1(\mathbb{R}^p,\lambda)$ such that $$\forall A\in\mathscr{B}(\mathbb{R}^p)\quad\mu(A)=\int_Ag \,\mathrm{d}\lambda~?$$

Answer 1

Every such measure is absolutely continuous w.r.t $\lambda$. If $\lambda$ is $\sigma$-finite, then the Radon-Nikodym theorem says that all measures that are absolutely continuous w.r.t. $\lambda$ are of this form.

EDIT: In light of the comment below, perhaps "measure with density" is more appropriate for the name. The absolute continuity is correct, though.