In a geometric measure theory (GMT) course I'm following this year, the professor told us about the Aronszajn measure, and asked us to go check by ourselves what it reprensents (the course was about measure theory in infinite dimensional Banach space). Unfortunalety, I didn't find on the internet what I was looking for, so I'd like to get some informations about these measures (including the definition), and references if possible.

Edit : Aronszajn measure are not defined, but there is a notion of negligeable sets. The definition is in the article mentionned by M. Peters or Handbook of the Geometry of Banach Spaces Volume 2 in the section of David Preiss. To be complete, I mention brielfly the definition. if $X$ is an infinite dimensional separable Banach space, and $(a_n)_{n\in\mathbb{N}}$ a dense sequence, a Borel subset $E\subset X$ is an Aronzajn null set if $E=\bigcup_{n\in \mathbb{N}}E_n$, $E_n$ is Borel, and for all $x\in X$, $\mathscr{H}^1(E_n\cap(x+\mathbb{R}a_n))=0$, where $\mathscr{H}^1$ is the one-dimenional Hausdorff measure.

nevera good idea to have the third word of anything one writes be an accronym unless the audience is very,verylimited. In any case, what does make me curious is if you asked this question to your professor right after googling and finding nothing! $\endgroup$ – Mariano Suárez-Álvarez Nov 7 '14 at 22:07