We say that a set $A \subset H$ of a (separable) Hilbert space is negligible if:
for every orthonormal basis $e_n \in H$ and every sequence $\epsilon_n \in \ell^2(\mathbb{N})$, if $C:= \prod_n [-\epsilon_n e_n, \epsilon_n e_n]$ and $\nu$ denotes the product measure associated to $dx/2\epsilon_n$, then $\nu((H\backslash A) \cap C)=0$.
I saw this in an old thesis that I can't find anymore. Could someone explain the statement
$\nu$ denotes the product measure associated to $dx/2\epsilon_n$, then $\nu((H\backslash A) \cap C)=0$
i.e., how exactly does the $\nu$ look like? I don't understand the $dx/2{\epsilon_n}$ part.
Does anyone have any more information or other terms that this concept is called?