/sci/ - Science & Math

Why is this wrong?

Consider the sequence [math]f_n:=f\chi_{[-n,n]}[/math], where [math]\chi_{A}[/math] is the indicator function on the set [math]A[/math]. Then (clearly?) [math]\lim \int f_n=\int f[/math]. Since for each [math]n[/math], the set [math][-n,n][/math] is compact, using the definition of the limit, this is our compact set