I look for an argument to this statement:
$ \int_a^x dx_1 \int_a^{x_1} K(x_1,t) dt= \int_a^xdt \int_t^x K(x_1,t) dx_1 $ It is certainly an integration by change of variables that I can not clarify
I look for an argument to this statement:
$ \int_a^x dx_1 \int_a^{x_1} K(x_1,t) dt= \int_a^xdt \int_t^x K(x_1,t) dx_1 $ It is certainly an integration by change of variables that I can not clarify
$a\leq x_1\leq x$ and $a\leq t\leq x_1$. So, one has that $t$ changes from $a$ to $x_1$ and $x_1$ changes from $a$ to $x$. It is the same that $t$ changes from $a$ to $x$ and $x_1$ changes from $t$ (it is more than $\min(a,t)=t$) to $x$(it less than $x$). You can draw a picture and everything will be evident.