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Uniform integrability under continuous functions

  1. Nov 2, 2012 #1
    Let X be a uniform integrable function, and g be a continuous function. Is is true that g(X) is UI?

    I don't think g(X) is UI, but I have trouble finding counter examples.

  2. jcsd
  3. Nov 3, 2012 #2
    This statement is true whenever \supp g (You can prove this with Heine Borel) or the range of {X_n} is compact.
    Since now you have the compactness relaxed, you can pursue that direction.

    Also, the foundation of this question is more towards Intro to Meas. Theory, you may consider re-post in the right domain.
    Last edited: Nov 3, 2012
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