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,