From: "Daniel Giaimo" Subject: Re: real anal Date: Sun, 11 Jun 2000 10:33:23 -0700 Newsgroups: sci.math Summary: [missing] wrote in message news:8h8qtp$vit$1@nnrp1.deja.com... > Anyone know of a book which proves (or know the proof of) if f:[a,b]->R > and f is lebesgue measurable, then, for every e>0, there exists a > continuous function h such that m{x:f(x)!=h(x)} f uniformly on F. 6. There exists a compact subset G of F s.t. m(F\G) < e/3. 7. By 5., f is continuous on G. 8. By Tietze's Extension Theorem, f|_G can be extended to a continuous function h on [a,b]. 9. m([a,b] \ G) < e, quod erat demonstrandum. --Daniel Giaimo