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[measure theory] measurable function f and simple function g

  1. Nov 22, 2009 #1
    Hi everyone!

    my problem:

    since every simple function is bounded, we at once know, that either is our function f, cause:
    [tex] - \epsilon + g(x) <= f(x) <= \epsilon + g(x)[/tex], so that's obviously not the problem here. this whole measure stuff doesn't get into my intuition and I don't have any idea how to try to solve this task. if i knew, that for each [tex]\epsilon[/tex] i could get a measurable function g, it would be obvious, that f is measurable too [wouldn't it?], but can i really always have a measurable function g?

    i would be very grateful for any hints. hope my english isnt terrible enough to disturb the sense of this post.

    rahl.
     
  2. jcsd
  3. Nov 26, 2009 #2
    Think about why pointwise limits of measurable functions ought to be measurable. Also, hopefully those simple functions are measurable.
     
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