Complex contour integral and measure theory

Question

Given $\gamma:[a,b]\rightarrow\mathbb{C}$ a rectificable curve and $f:\Omega\subseteq\mathbb{C}\rightarrow\mathbb{C}$ a continuous function s.t. $\gamma([a,b])\subseteq\Omega$ it is standard to define: $$\int_{\gamma}f(z)\; dz:=\int_a^bf(\gamma(t))\gamma'(t)\; dt$$ Now I have studied complex measures and I was wandering if this contour integral could be seen in a measure theoretic way, in the same way as you can see standard line integrals in $R^n$ as integrals wrt the Hausdorff measure. In other words I would like to know if exists a complex measure $\mu$ s.t.: $$\int_{\gamma}f(z)\; dz=\int_\gamma f \; d\mu$$ Unfortunately I could not find anything about this. Can you give me same reference/explaination?