What is the intuition behid the constant invariant quantities and why do we need it? How is this related with probability theory?
I was solving some maximization problem and when I saw the answer, the author mendtioned that since the quantity $\mathbf{B}\in L^2(\Omega,\mathbb{F},\mathbb{P})$ is constant invariant then it holds that $\mathbb{E}(\mathbf{B})=0$ and she only considers - uses the variance of the r.v. to find the maximum.