If a sequence converges in L2 and we compose every function with a non-singular function, does it still converge? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T11:51:59Z http://mathoverflow.net/feeds/question/73130 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73130/if-a-sequence-converges-in-l2-and-we-compose-every-function-with-a-non-singular-f If a sequence converges in L2 and we compose every function with a non-singular function, does it still converge? BBB 2011-08-18T09:02:55Z 2011-08-18T17:19:14Z <p>Let $F:(0,1)\rightarrow (0,1)$ be a non-singular function with respect to the lebesgue measure $\mu$ (so $\mu\sim\mu \circ F$ ) . let $\lbrace f_n/n\in N\rbrace\subset L^{2}([0,1])$ be a sequence of simple integrable functions and $f\in L^{2}([0,1])$ such that $f_n\rightarrow f$ in the 2-norm. is it correct that also $f_n\circ F\rightarrow f\circ F$ ?</p> <p>If not, what are the conditions on $F$ such that this inplication is correct?</p>