View source for Hereditary system of sets

{{Stub page|Needs linking to where it is used, notes on a sort of "power-set" like construct.|grade=B}}
: '''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==
A collection of [[set|sets]], {{M|\mathcal{H} }} is said to be ''hereditary'' if{{rMTH}}:
* {{M|\forall A\in\mathcal{H}\forall B\in\mathcal{P}(A)[B\in\mathcal{H}]}}, in words:
** for all sets {{M|A\in\mathcal{H} }} all subsets of {{M|A}} must be in {{M|\mathcal{H} }}
==See also==
* [[Hereditary sigma-ring|Hereditary {{sigma|ring}}]] - the motivation for this definition.
==References==
<references/>
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