Title: S-measures

Abstract: S-measures are standard measures constructed using nonstandard
analysis; they are the restriction of the Loeb measure to a
sub-sigma-algebra which is close in some sense to a given standard
sigma-algebra, and have proved useful for certain kinds of limit arguments.
I will introduce S measures, give a couple of graduate analysis level applications,
and then give a proof of the Birkhoff Ergodic Theorem that combines
S-measures with the main trick in T. Kamae’s proof of the result.