Why are absolutely continuous measures called that way? Let $X\subseteq \Bbb{R}^n$ and $\mathcal{B}(X)$ the borelian set for $X$. Let $\mu$ and $\nu$ be two measures on $(X,\mathcal{B})$. We say that $\mu$ is absolutely continuous with respecto to $\nu$ (denoted by $\mu\ll \nu$) if $\forall A\in\mathcal
{B}(X),\; \mu(A)=0\implies \nu(A)=0$.
Generally, continuity refers to some sort of smoothness of a function: small variations on domain gives an small variation on co-domain. I don't see how this definition fits this category which leads me to wonder, why are absolutely continuous measures called that way? I'm looking for maybe an historical answer (the reason why it started being called that way) or an answer that appeals to the definition itself (something on the definition which makes it reasonable to be called that way).

Comment.  I guess you would need to consult G. Vitali.  (1905, coined the term "absolutely continuous function"; later "absolutely continuous measure" was modeled on that.)
From Mathwords:

ABSOLUTE CONTINUITY. The concept was introduced in 1884 by E. Harnack "Die allgemeinen Sätze über den Zusammenhang der Functionen einer reellen Variabelen mit ihren Ableitungen. II. Theil." Math. Ann. 21, (1884), 217-252. The term was introduced in 1905 by G. Vitali. In the meantime several mathematicians had used the concept. See T. Hawkins Lebesgue's Theory of Integration.

