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Math Help - is R Lebesgue-measurable?

  1. #1
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    is R Lebesgue-measurable?

    Hi! I want to ask if is R^2 is Lebesgue-measurable?
    If yes why?
    This is true also for R, R^3 and so on?
    Are they Peano-Jordan measurable?

    I thought they were because their complementar is empty. Sorry for my english. Thank you.
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  2. #2
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    Quote Originally Posted by venturozzaccio View Post
    Hi! I want to ask if is R^2 is Lebesgue-measurable?
    If yes why?
    This is true also for R, R^3 and so on?
    Are they Peano-Jordan measurable?

    I thought they were because their complementar is empty. Sorry for my english. Thank you.
    If you have a sigma algebra on any space it will contain the entire space. This holds for any sigma algebra so the whole space is always measurable.
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