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Math Help - Measure Space Definition Question

  1. #1
    MHF Contributor Swlabr's Avatar
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    Measure Space Definition Question

    When we define a measure space (X, \Sigma, \mu) do we take \mu to be a (positive) measure ( \Sigma the measurable sets)? That is, is \mu a map \mu: \Sigma \rightarrow [0, +\infty]?

    Or am I just confused? Will it just depend on who is defining it? On the book I am reading? Or is it by convention?
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  2. #2
    Moo
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    Hello,

    \Sigma will be the set ( \sigma-algebra) of all the \mu-measurable sets.

    But then I don't know if talking about a measure space this way implies that the measure is positive... In my opinion, unless clearly stated, \mu would be a positive measure.
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