Let $X$ be a set of finite (positive) measure. Let $C$ be the collection of all finite subsets of $X$ and their complements in $X$. Is $C$ an algebra of sets? Is $C$ a $\sigma$-algebra? Explain.
Real analysis: collection of sets - sigma-algebra or not?
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real-analysis
measure-theory
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4Ancient Proverb: OP gives orders, OP needs no answers. – 2012-03-24
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0What measure is defined on $X$? – 2012-03-24
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1For algebra of sets, look at the definition. It will be easy for you to verify that the conditions of the definition are satisfied. For $\sigma$-algebra, the answer in general is no. Let $X$ be the positive integers. The measure is irrelevant, but if you want one, put mass $1/2$ at $1$, mass $1/4$ at $2$, and so on. Now is $C$ closed under countable union? – 2012-03-24