#noindex
## =측도공간,measure_space =,measure_space 측도공간 measure_space
측도 공간
측도공간
measure space


정의는 [[가측공간,measurable_space]]
과 [[https://terms.naver.com/entry.naver?docId=3405357&cid=47324&categoryId=47324 수학백과: 측도]] 의 앞부분 정의 참조.
 이 정의에 가산가법성([[countable_additivity]]) 나옴 - rel [[가법성,additivity]]


총 측도가 1인 경우 [[확률공간,probability_space]]임....? chk


//mw
nonnegative_measure 를 possess한(가진??) [[가측공간,measurable_space]]이 바로 '''측도공간'''.

//from ency. of math
{
'''측도공간'''은 triple $(X,\mathcal{A},\mu)$
 $X$ : a [[집합,set]]
 $\mathcal{A}$ : a [[시그마대수,sigma-algebra]] of its [[부분집합,subset]]s
 $\mu$ : $\mathcal{A}\to[0,+\infty]$ a [[측도,measure]]
그래서, '''측도공간'''은 [[가측공간,measurable_space]] 하나와 [[측도,measure]] 하나로 구성.
위의 표기법을 $(X,\mu)$ 로 줄여서 $\mu$ is a measure on $X$ 라 하거나, $X$ 로 줄이기도 함.
}

전체측도가 1이면 [[확률공간,probability_space]]? chk (via that page)

MKLINK
[[거리공간,metric_space]]

----
[[WtEn:measure_space]]
= https://en.wiktionary.org/wiki/measure_space

----
https://mathworld.wolfram.com/MeasureSpace.html

https://encyclopediaofmath.org/wiki/Measure_space
 "...Thus, a '''measure space''' consists of a measurable space and a measure."
 i.e. [[가측공간,measurable_space]]과 [[측도,measure]]로 구성.

https://everything2.com/title/measure+space

https://ncatlab.org/nlab/show/measure+space

[[WpEn:Measure_space]]
= https://en.wikipedia.org/wiki/Measure_space

...
Ndict:측도공간 Google:측도공간 Naver:측도공간

Page name via KmsK:측도공간 = https://www.kms.or.kr/mathdict/list.html?key=kname&keyword=측도공간
{ [[Date(2023-11-14T09:55:07)]] 현재 저기 9개:
complete measure space	완비측도공간 // [[완비측도공간,complete_measure_space]] =완비측도공간,complete_measure_space =,complete_measure_space 완비측도공간 complete_measure_space
{
complete measure space
'''complete measure space''' 

[[WtEn:complete_measure_space]] = https://en.wiktionary.org/wiki/complete_measure_space x 2023-11-14

....
완비측도공간 
Ndict:완비측도공간 
Ggl:완비측도공간

"complete measure space"
Ndict:"complete measure space"
Ggl:"complete measure space" 
Ggl:"definition of complete measure space"

} // complete measure space = 완비측도공간
finite measure space	유한측도공간
measure space	측도공간 // [[측도공간,measure_space]]
probability measure space	확률측도공간 // [[확률측도공간,probability_measure_space]] w ... Ggl:확률측도공간
quasi measure space	준측도공간
space of generalized measures	일반화된 측도공간
standard measure space	표준측도공간 // Ggl:표준측도공간
Wiener measure space	위너 측도공간 // Ggl:"Wiener measure space"
Yeh-Wiener measure space	예-위너 측도공간 // Ggl:"Yeh-Wiener measure space"
}

Up: [[측도,measure]] [[측도론,measure_theory]] [[공간,space]]
= wikiadmin =
== logs ==
[[Date(2023-11-14T09:48:18)]] 로컬에서 RR로 복사함.