Hello,
Is there a way to find the class of all bounded functions $f(w,y)$ which satisfies the following inequality:
$$ \int\limits_{-\infty}^{+\infty} f(w,y) ~\mathcal{N}(y,w,1) dy >0 ~~~~\forall w $$
it is assumed that the function $f(w,y)$ is integrable w.r.t. to the Gaussina pdf $\mathcal{N}(y,w,1) $. For instance, the function $I_A(y)-0.5$, where $I_A$ is the indicator function over the set $A={(w,y): w-a\leq y<\infty}$ satisfies the inequality for each scalar $a>0$.
