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Measure Theory & Borel Sets

March 15, 2010 at March 15, 2010 · Filed under enart.nnxj.comedit

  • mu is a measure on the Borel sets of a separable, complete, metric space X such that mu(X) = 1 Is it possible to choose a Borel set of a prescribed measure (e.g. For any c in the unit interval there exists a Borel set E in X such that mu(E) = c). If so, please prove. The question is related to a problem from Halmos' Measure Theory text, chapter 2 sec 9 #10


  • Hello Mathtalk, I appreciate your posting a comment on my question. I'm not quite sure however, how your hint connects to a counterexample. In any case, I'm no longer convinced that this result is necessary to the problem, so I'm cancelling the question. Regards halmosreader1-ga


  • Perhaps I've missed a critical part of the problem, but I think there is a trivial counterexample. Hint: Pick point x in X. regards, mathtalk-ga







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