Talk:Egorov's Theorem

The theorem, as presently stated here, is "on a set of finite measure, pointwise a.e. convergence implies uniform a.e. convergence".

This is not true. See for example $f_n (x) = n \chi_{[2^{-n}, 2^{-(n+1)}]}(x)$ on the set $[0, 1]$. This function converges pointwise, and thus pointwise a.e., but it does not converge uniformly a.e. (Credit to Terrence Tao for the counter-example.)

The proper statement of Egorov's Theorem is "on a set of finite measure, pointwise a.e. convergence implies almost uniform convergence." Lilred (talk) 08:15, 1 November 2016 (EDT)