I see this page https://mathoverflow.net/questions/158270/ordinary-least-square-and-random-projection, and I am thinking that how $L^2$ integrable random variables be regarded as projections over a defined filtration sequence $\mathcal{F_n}$ ?

It seems that a vector space of square integrable random variables defined on the same probability space is not enough? 
Is there existing literature addressing a formalism of this projection view? Thank you!