uniform boundedness - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-22T19:14:48Z http://mathoverflow.net/feeds/question/81426 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81426/uniform-boundedness uniform boundedness Moe 2011-11-20T14:46:01Z 2011-11-20T14:46:01Z <p>" If we have a sequence of complex measurable funtions {f_n} in a FINITE measurable space (X,M,u) , such that sup{ |f_n (x)| : n is N } &lt; infinity , x is in X </p> <p>then to each epsilon>0 there exists a set E and a number 0 <p>u(E)&lt; epsilon |f_n (x)| &lt;= B , for all n and x in the complement of E </p> <p>what if u(X) is infinite ? "</p>