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Weak limit of abs. continuous measures

  1. Sep 23, 2011 #1
    say we have a sequence of probability measures on R, such that each one is abs. continuous wrt the Lebesgue measure...

    is it possible that these measures converge weakly to a measure which is _not_ abs. continuous wrt the Lebesgue measure?
     
  2. jcsd
  3. Sep 26, 2011 #2
    yes, e.g. normal distribution as variance goes to zero.
     
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