Absolutely Continuous Probability Measure on Euclidean Space

In the setting of Probability Measures on Euclidean Space and Random Vectors: Standing Notation, which has the notation of Product Measures and Lebesgue Measure on ℝⁿ: Standing Notation and Background in force, let $d\in\mathbb{N}$ satisfy $1\le d$, let $\mathcal{B}(\mathbb{R}^{d})$ be the Borel $\sigma$-algebra of $\mathbb{R}^{d}$ and $\lambda_{d}$ its Lebesgue measure, and let $\mu$ belong to the set $\mathcal{P}(\mathbb{R}^{d})$ of probability measures on $\mathbb{R}^{d}$.

(Absolutely continuous measure)(i) The measure $\mu$ is absolutely continuous if

$$\mu(B)=0\qquad\text{for every }B\in\mathcal{B}(\mathbb{R}^{d})\text{ with }\lambda_{d}(B)=0 .$$