A First Course in Stochastic Processes (Karlin, S.) defines, for increasing, right-continous functions $A,B$ with $A(0)=B(0)=0$, the convolution $A*B$ as
$$A*B(t)=\int_0^t B(t-y)dA(y).$$
In addition, for any function $c(t)$ (assumed reasonably smooth and bounded on finite intervals) it defines $B*c$ as
$$B*c(t)=\int_0^t c(t-y)dB(y).$$
It then states that the following is easy to verify:
$$A*(B*c)=(A*B)*c.$$
I am having trouble proving this statement, in particular due to the notation of the Lebesgue-Stieltjes integral. Here is what I have:
\begin{align} A*(B*c)(t)=&\int_0^tB*c(t-y)dA(y)\\ =&\int_0^t\int_0^{t-y}c(t-y-z)dB(z)dA(y). \end{align}
However, I cannot figure out the steps required to achieve equation with the RHS. If I try to work out the RHS, I obtain: \begin{align} (A*B)*c(t)=&\int_0^t c(t-y)d[A*B(y)], \end{align} of which I do not know how I should interpret it.