Here's something I've encountered in some code I'm writing.
p, q are two real values in the range [0..1]
m is the average of p, q, i.e. (p+q)/2,
Can it ever be the case that:
p^p * q^q < m^(p*q)
Where '^' is exponentiation, not XOR?
Anyway, the point is, if the above relation can NEVER be true, then I can make an enormous optimization somewhere.
I'm sure somebody in the infotheory literature has already proved/disproved this, but I haven't found it yet.