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Question about Lp spaces

  1. Jan 12, 2009 #1
    Im an applied statistician who hasnt looked at this stuff in years (And even then never took a class in it formally). So try and forgive me if my language is sloppy.

    Consider the space of all d-dimensional bounded random vectors, L_infinity. Its Banach, hence complete and closed.

    Consider a single fixed d-dimensional random vector in L1. Lets call it X.

    Is the set

    {aX : a is in L_infinity} necessarily closed? Here Im considering the dot product so that aX is a random variable.

    Any help, references, etc would be greatly appreciated.

    Best regards,
  2. jcsd
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