Is the Hausdorff measure absolutely continuous with respect to the lebesgue measure? $H^{d-1} \ll \lambda^d$

Question

I'm sure this is just basic theory but I can't find this ANYWHERE. Is it true that $$ H^{d-1} \ll \lambda^d $$ where $H^{d-1}$ is the $(d-1)$-dimensinal Hausdorff measure and $\lambda^d$ is the $d$-dimensional Lebesgue measure.

• If this is true, does the Radon-Nykodym derivative $\frac{d H^{d-1}}{d \lambda^d}$ exist? And what can we say about it?
• If this is not true, is there a similar relation? For instance with different dimensions.