My research require me to integrate this separable function $f\left( {x,y,z,t} \right) = f\left( x \right)f\left( y \right)f\left( z \right)f\left( t \right)$ over the region $D = {D_1} \cap {D_2}$
Where ${D_1} = \left\{ {z > \frac{a}{x} \cap x > 0 \cap z > 0} \right\}$ and ${D_2} = \left\{ {z > byt + \frac{c}{x} \cap x > 0 \cap y > 0 \cap z > 0 \cap t > 0} \right\}$.
From my domain knowledge, the individual function $f\left( x \right),f\left( y \right),f\left( z \right),f\left( t \right) > 0$ on their corresponding domain $x,y,z,t \in \left[ {0,\infty } \right]$
Does the integration of $f\left( {x,y,z,t} \right)$ over the region $D' = \left\{ {z > byt + Max\left( {\frac{a}{x},\frac{c}{x}} \right) \cap x > 0 \cap y > 0 \cap z > 0 \cap t > 0} \right\}$ is equivalent to the integration over the region $D$ in $D = {D_1} \cap {D_2}$ ?
Furthermore, what would be the correct integration bound ?
Please help me !
Thank you for your enthusiasm !
Edit: I forgot to add the fact that $a,b,c$ are three positive real number