Abstract: It may well be the most important result proved by a
Hungarian mathematician that every locally compact group admits a
natural invariant measure, the so called Haar measure. However, it is
also known that if a Polish group is not locally compact (think of
e.g. $C[0,1]$ or the permutation group $S_\infty$) then there is no
Haar measure on it. However, as Christensen showed, the notion of a
Haar \emph{nullset} has a very well-behaved generalisation, hence it
makes sense to talk about almost every continuous function or almost
every permutation. After surveying this notion we will discuss
innocent-looking problems like "Is every nullset contained in a
$G_\delta$ nullset?", then we will describe various properties of
almost every continuous function.

You can watch the lecture here:

http://www.youtube.com/watch?v=VvIr2N27Cv0&list=PL_0phSnA7tyQJDn-5hacAuELRteKNuyl-&index=3