Difference between revisions of "Hereditary system of sets"
From Maths
(Created page with "{{Stub page|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 ref...") |
m |
||
| Line 1: | Line 1: | ||
| − | {{Stub page|Needs linking to where it is used, notes on a sort of "power-set" like construct.}} | + | {{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 | : '''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
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
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, H is said to be hereditary if[1]:
- ∀A∈H∀B∈P(A)[B∈H], in words:
- for all sets A∈H all subsets of A must be in H
See also
- Hereditary σ-ring - the motivation for this definition.
References
| ||||||||||||||||||||
