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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.

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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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 answer finishes by saying he would be interested if…
Stan Shunpike
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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 $(0,1]$ you'll get the closed set $[a, b]$. This is…
Dilan
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On the definition of semi-algebra

I found two definitions in some textbooks. One is defined as follows: A collection $\mathscr{C}$ of subset of $X$ is called a semi-algebra if (a) $\emptyset \in \mathscr{C},$ (b) if $A, B\in \mathscr{C},$ then $A\cap B\in \mathscr{C},$ (c) for $A\in…
ljjpfx
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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
antonis34
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