In Terence Tao's book "An Introduction to Measure Theory" (Pg.6), the measure of a $d$-dimensional box $B$ is given by
$$|B| = \lim_{N\to\infty}\frac{1}{N^d}\#\left(B\cap\tfrac{1}{N}\mathbb Z^d\right),$$
However, should it be written as the following instead?
$$|B| = \lim_{N\to\infty}\frac{1}{N^d}\#\left(B\cap\tfrac{1}{N^{\color{red}d}}\mathbb Z^d\right),$$
i.e. should we also need $N^{\color{red}d}$ instead of $N$ inside the "$\#\left(...\right)$"?