Lebesgue Measure of Scalar Multiple

Theorem
Let $\lambda^n$ be the $n$-dimensional Lebesgue measure on $\R^n$ equipped with the Borel $\sigma$-algebra $\mathcal B \left({\R^n}\right)$.

Let $B \in \mathcal B$, and let $t \in \R_{>0}$.

Then $\lambda^n \left({t \cdot B}\right) = t^n \lambda^n \left({B}\right)$, where $t \cdot B$ is the set $\left\{{t \mathbf b: \mathbf b \in B}\right\}$.