1. The problem statement, all variables and given/known data A stereotypical problem in measure theory. fn(x)=1 when 0<=x<=1/n =0 when 1/n<x<=1 f(x)=0 0<=x<=1 Under the lebesgue measure Does fn converge to f? a. for all x b. almost everywhere c. uniformly on [0,1] d. uniformly almost everywhere on [0,1] e. almost uniformly f. in measure g. in Lp 2. Relevant equations 3. The attempt at a solution My guess of the answer would be: a. for all x: No, doesn't converge at x=0 b. almost everywhere: Yes, x=0 has lesbesgue measure 0 c. uniformly on [0,1]: No d. uniformly almost everywhere on [0,1]: No e. almost uniformly: Yes f. in measure: Yes g. in Lp: shouln't it depend on p? no idea.