Thread: Measurable Functions

Hi, math geniuses, Im having trouble with these two real analysis problems.

1) F Measurable, h in R, prove that g(x) = f(x+h) is measurable.

2) f continuous in almost every point. => f is measurable.

Thanks!

Do you mean Borel or Lebesgue measurable? For the first question, write it as a limit of simple functions.

the definition of Measurable function with Lebesgue Measure.