## Functions with positive expected value w.r.t a Gaussian pdf

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 $a>0$.

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For what it's worth, this question is also cross-posted to math.SE: math.stackexchange.com/questions/7889/… @vatna: mind explaining why the question is marked CW? – Willie Wong Oct 26 2010 at 10:08