Difference between revisions of "Hereditary system of sets"
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: '''Note: ''' see [[hereditary]] for different uses of the word, this page refers to ''hereditary'' as used in [[Measure Theory (subject)|Measure Theory]] and ''[[Hereditary (measure theory)]]'' redirects here | : '''Note: ''' see [[hereditary]] for different uses of the word, this page refers to ''hereditary'' as used in [[Measure Theory (subject)|Measure Theory]] and ''[[Hereditary (measure theory)]]'' redirects here | ||
==Definition== | ==Definition== | ||
Latest revision as of 21:25, 19 April 2016
Stub grade: B
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Needs linking to where it is used, notes on a sort of "power-set" like construct.
- Note: see hereditary for different uses of the word, this page refers to hereditary as used in Measure Theory and Hereditary (measure theory) redirects here
Definition
A collection of sets, [ilmath]\mathcal{H} [/ilmath] is said to be hereditary if[1]:
- [ilmath]\forall A\in\mathcal{H}\forall B\in\mathcal{P}(A)[B\in\mathcal{H}][/ilmath], in words:
- for all sets [ilmath]A\in\mathcal{H} [/ilmath] all subsets of [ilmath]A[/ilmath] must be in [ilmath]\mathcal{H} [/ilmath]
See also
- Hereditary [ilmath]\sigma[/ilmath]-ring - the motivation for this definition.
References
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