strick inequality for Fatou theorem - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T11:42:10Z http://mathoverflow.net/feeds/question/24787 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/24787/strick-inequality-for-fatou-theorem strick inequality for Fatou theorem Walter 2010-05-15T17:56:30Z 2010-05-15T18:01:41Z <p>If $f_n=1_{(n,n+1)}(x)$, where $1_A(x)$ is the indicator function. Why is $f_n \rightarrow0$? Same is true for $f_n=1_{(n,\infty)}$.</p> <p>i just dont get it.</p> <p>i thought $f_n$ was always 0 for all n so i think $f_n\rightarrow1$ but its not the case. i try to reason it by the integral which is 1 for all n but then i dont go anyway.</p> http://mathoverflow.net/questions/24787/strick-inequality-for-fatou-theorem/24788#24788 Answer by Henri for strick inequality for Fatou theorem Henri 2010-05-15T18:01:41Z 2010-05-15T18:01:41Z <p>This is just the definition of convergence for sequences of functions : $\forall x \in \mathbb R, \lim_{n \to+\infty} f_n(x) =0$, which is of course the case here, all sequences $(f_n(x))$ being stationary. </p>