Logic Seminar
Patrick Speissegger
McMaster University
A Borel Lemma for o-minimal structures
Abstract: Let f be a totally defined real-valued function on the real line. Borel's Lemma states that if f is increasing
and everywhere greater than or equal to 1, and if r>1 is fixed, then the set {x: f(x + 1/f(x)) >= r f(x)} has
outer measure at most r/(r-1). Recently, Chris Miller conjectured that a suitably restated version of Borel's
Lemma was true in the o-minimal setting. Interestingly, the proof of this version appears to be more
elementary for exponential o-minimal structures than for power-bounded ones. (Joint work with Alf
Dolich and Chris Miller)
Tuesday April 11, 2006 at 4:00 PM in SEO 427