*[Removed – T.]*

Where the separability assumption were used in the first proof of Theorem 2?

*[The first proof is in fact valid for inseparable Hilbert spaces also. -T]*

[* To show , one can either use Jensen, or else apply Cauchy-Schwarz to the functions and . -T*]

(https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/#as-rem), which is for the discrete random variables. Are they essentially the same? ]]>