Given Probability space $(\Omega, \mathcal{F}, \mathbb{P})$, Suppose $\mathbb{E}[X^2] < \infty .$ Let $$ Z:=\mathbb{E}[X|\mathcal{F}] $$ Show that $$\mathbb{E}[(X-Z)^2]=\min_{y \in m\mathcal{F}} \mathbb{E}[(X-Y)^2]. $$
I don't know how to approach this problem. Actually cannot understand the condition $ Z:=\mathbb{E}[X|\mathcal{F}] $ because then it will be $Z=X$ I guess? Someone could please help? Thanks in advance.