If f(x,y) is nonnegative decrasing in x for fixed y, 0<x<1, 0<y<0.4 say, then one can show that the quadruple integral
.
Is it true that
.
for any non-negative function g(x,y) ? I think it is but can't seem to come up with a simple proof without going through the process of simple functions etc. Other assumptions are
f and g are bounded by 1, continously differentiable with respect to each parameter.
Thanks,