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Questions tagged [semialgebras]

A semialgebra on a set is class of subsets of the set. It contains the original set and the empty set. Further the class is closed under finite intersections and any difference of two sets belonging to it can be written as a finite union of mutually disjoint elements of it. It is used especially in the theory of measures and probabilities.

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How do we prove that all intervals contained in [0,1] is a semi-algebra?

Well, I know the definition of semi-algebra but I cannot prove that all intervals contained in [0,1] is a semi-algebra
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Proving that the set of all finite disjoint unions of mutually disjoint sets in a Semi Algebra, is the Algebra generated from the Semi Algebra

I am reading this book called as A probability path, by Sidney I Resnick. In this book he states the following axiom: Axiom And he goes on to prove it as follows: Proof Page 1 Proof Page 2 Can ...
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Symbol in Theorem A.1.1 in Durrett's Probability (4th edition)

The highlighted symbol is found in Durrett's "Probability: Theory and Examples" (4th edition). What does it mean?
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Semigroups and measure

A semialgebra $\mathcal S$ is a Set of subsets such that: $\emptyset, X \in\mathcal S$ where $X$ is the Universe. If $A,B \in\mathcal S$, then $A \cap B \in\mathcal S$ If $A \in\mathcal S$, then $A^c ...
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Question about the definition of a semialgebra

This question has been asked here Question about definition of Semi algebra The OP unfortunately has selected an incorrect answer and no agreed upon correct answer has been given. The most upvoted ...
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Proving a semialgebra

The sets of the form of all $(a, b]$ intervals in $(0, 1]$ is given to be a semialgebra. If you take an inf intersection of $(\frac{a -1}{n}, b]$, for $n \to \infty$, for some valid $a$ and $b$ in $(...