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Lebesgue measure on sigma algebra, help ........... Which of the following are sigma algebras? reply with justification please.

  1. All subsets in rational numbers
  2. { {0},{1},{0,1} }in space {0,1}
  3. all intervals [x,y) x,y elements of [0,1] and all their unions in the space [0,1)
  4. all subsets of [0,1]
  5. all open subsets in real line(with usual metric)
  6. all finite subsets and all subsets with finite complement in rationals.

please help thank you.

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    In each case, you must specify what the entire space is. You did this in #2; this is a sigma algebra. This leaves an ambiguity in #1.2012-09-30
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    Welcome to M.SE! You will receive better answers if you provide context about where you have encountered a problem, what your background is and what you have tried so far. As to your question, it has little to do with Lebesgue measure. A $\sigma$-algebra has to contain $\emptyset$ and the whole space- it has to contain the complement of every set it contains. And it has to contain the union of every sequence of sets it contains. Try to check this in each case.2012-09-30
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    No, a $\sigma$-algebra contains $\emptyset$.2012-09-30
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    @Berci What does your *no* refer to?2012-09-30

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