Talk:Egorov's theorem

I can't understand this formulation. It should say, roughly, that the sequence almost everywhere converges uniformly.

Charles Matthews 10:26, 20 Apr 2005 (UTC)

I don't understand what you are saying. Can you be more specific about what you think the article ought to say? Thanks. NatusRoma 20:50, 22 Apr 2005 (UTC)
Charles, I don't believe you are right. Egorov's theorem says that pointwise convergence implies that for any e>0, there is a set whose complement has measure at most e, on which convergence is uniform. This isn't the same as uniform convergence almost everywhere. This means there is a nullset, outside of which convergence is uniform. One can't take the intersection of the sets of measure say, 1/n, outside of which convergence is uniform. That intersection is a nullset, but convergence isn't necessarily uniform outside it. This is because the rate of convergence could be different on each of the sets of the sequence. You cam probably work out an example using your favourite example of pointwise convergence which isn't uniform. HTH. Via strass 20:17, 30 April 2007 (UTC)