measure
측도
측도
rel. measure_zero measure zero ( https://mathworld.wolfram.com/MeasureZero.html )
https://ko.wikipedia.org/wiki/영집합
Up: 널,null 집합,set 측도론,measure_theory
}
표현들
almost everywhere, a.e. - 측도공간,measure_space에 대해, 널집합,null_set을 제외한
almost surely, a.s.
측도론
measure theory
Up: 널,null 집합,set 측도론,measure_theory
}
표현들
almost everywhere, a.e. - 측도공간,measure_space에 대해, 널집합,null_set을 제외한
almost surely, a.s.
![YouTube: YouTube:](/wiki/imgs/interwiki/youtube-16.png)
![YouTube: YouTube:](/wiki/imgs/interwiki/youtube-16.png)
Contents
- 1. Sub:
- 1.1. Hausdorff measure
- 1.2. Martin measure
- 1.3. Borel measure
- 1.4. 르베그 측도 Lebesgue measure
- 1.5. discrete measure
- 1.6. signed measure
- 1.7. probability measure
- 1.8. discrete measure
- 1.9. measure space
- 1.10. measurable space
- 1.11. Wiener measure
- 1.12. positive measure
- 1.13. counting measure
- 1.14. outer measure
- 1.15. premeasure
- 1.16. Caratheodory measure
- 1.17. 셈 측도, counting measure
- 1.18. ADD_MEASURE_HERE
- 1.19. ADD_MEASURE_HERE
- 1.20. ADD_MEASURE_HERE
- 1.21. ADD_MEASURE_HERE
- 1.22. ADD_MEASURE_HERE
- 1.23. ADD_MEASURE_HERE
- 2. Topics: / REL / MKL
- 3. Foot
1.5. discrete measure ¶
discrete measure
discrete_measure =,discrete_measure =,discrete_measure . discrete_measure
discrete measure
이산측도[1]
discrete_measure =,discrete_measure =,discrete_measure . discrete_measure
discrete measure
이산측도[1]
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
https://ja.wikipedia.org/wiki/離散測度
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"discrete measure"
1.6. signed measure ¶
signed measure
부호측도 (wk)
부호있는측도 ?
signed measure
signed_measure =,signed_measure =,signed_measure . signed_measure
signed_measure
부호측도 (wk)
부호있는측도 ?
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
signed_measure =,signed_measure =,signed_measure . signed_measure
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Signed_measure
https://ko.wikipedia.org/wiki/부호_측도
https://encyclopediaofmath.org/wiki/Signed_measure
signed measure
signed measure
"signed measure"
https://ko.wikipedia.org/wiki/부호_측도
https://encyclopediaofmath.org/wiki/Signed_measure
generalized measure, real valued measure, charge
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"signed measure"
1.7. probability measure ¶
probability_measure =,probability_measure =,probability_measure . probability_measure
probability_measure
https://en.wikipedia.org/wiki/Probability_measure
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://en.wikipedia.org/wiki/Probability_measure
확률측도 ?
"probability measure"
"probability measure"
1.8. discrete measure ¶
discrete_measure =,discrete_measure =,discrete_measure . discrete_measure
이산측도?
discrete_measure
https://encyclopediaofmath.org/wiki/Discrete_measure
discreteness - maybe 이산성,discreteness
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://encyclopediaofmath.org/wiki/Discrete_measure
discreteness - maybe 이산성,discreteness
1.9. measure space ¶
measure space
measure_space =,measure_space =,measure_space . measure_space
measure_space
측도공간?
measure space
measure_space =,measure_space =,measure_space . measure_space
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
측도공간?
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WpEn: WpEn:](/wiki/imgs/interwiki/wpen-16.png)
= https://en.wikipedia.org/wiki/Measure_space
이것의 중요한 example: 확률공간,probability_space =확률공간,probability_space =,probability_space 확률공간 probability_space { MKL 확률측도,probability_measure https://simple.wikipedia.org/wiki/Probability_space https://en.wikipedia.org/wiki/Probability_space https://ko.wikipedia.org/wiki/확률_공간
확률공간
확률공간 확률공간 }
no wk. 2023-08-28
https://encyclopediaofmath.org/wiki/Measure_space![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
no wk. 2023-08-28
https://ncatlab.org/nlab/show/measure space
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
"measure space"
Cmp measurable_space // 일단 바로아래section
1.9.1. complete measure space ¶
https://en.wikipedia.org/wiki/Complete_measure_space
"is a measure space in which every subset of every 널집합,null_set is measurable (having measure zero)."
https://ko.wikipedia.org/wiki/완비_측도_공간1.10. measurable space ¶
measurable space
measurable_space =,measurable_space =,measurable_space . measurable_space
가측공간?
measurable space
measurable_space
https://mathworld.wolfram.com/MeasurableSpace.html
https://en.wikipedia.org/wiki/Measurable_space
https://ko.wikipedia.org/wiki/가측_공간
https://encyclopediaofmath.org/wiki/Measurable_space
measurable_space =,measurable_space =,measurable_space . measurable_space
가측공간?
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
https://mathworld.wolfram.com/MeasurableSpace.html
https://en.wikipedia.org/wiki/Measurable_space
https://ko.wikipedia.org/wiki/가측_공간
https://encyclopediaofmath.org/wiki/Measurable_space
Also: Borel space // Also: Borel_space
https://ncatlab.org/nlab/show/measurable spacemeasurability ?
measurability
measurability
measurability
measurability
measurability
measurability
measurable space
measurable space
"measurable space"
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Ndict: Ndict:](/wiki/imgs/interwiki/ndict-16.png)
![KmsE: KmsE:](/wiki/imgs/interwiki/kmse-16.png)
![NdEn: NdEn:](/wiki/imgs/interwiki/nden-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
![WtEn: WtEn:](/wiki/imgs/interwiki/wten-16.png)
![Ggl: Ggl:](/wiki/imgs/interwiki/ggl-16.png)
![Bing: Bing:](/wiki/imgs/interwiki/bing-16.png)
"measurable space"
Cmp measure_space // 일단 바로위section
REL 가측집합,measurable_set { https://encyclopediaofmath.org/wiki/Measurable_set
rel
measurable subset measurable_subset https://ncatlab.org/nlab/show/measurable subset "measurable subset" }
REL 가측집합,measurable_set { https://encyclopediaofmath.org/wiki/Measurable_set
rel
measurable subset measurable_subset https://ncatlab.org/nlab/show/measurable subset "measurable subset" }
1.13. counting measure ¶
1.16. Caratheodory measure ¶
Caratheodory measure
Carathéodory measure
Carathéodory measure
Caratheodory_measure =,Caratheodory_measure =,Caratheodory_measure . Caratheodory_measure
{
https://mathworld.wolfram.com/CaratheodoryMeasure.html
{
https://mathworld.wolfram.com/CaratheodoryMeasure.html
}
1.17. 셈 측도, counting measure ¶
counting measure
counting_measure
counting_measure
https://namu.wiki/w/셈 측도
{
dimensionless. (tmp curr.
차원,dimension?action=highlight&value=dimensionless#s-4 / linked to
무차원량 )
}
{
dimensionless. (tmp curr.
![VG: VG:](/wiki/imgs/interwiki/vg-16.png)
![Namu: Namu:](/wiki/imgs/interwiki/namu-16.png)
}
2. Topics: / REL / MKL ¶
----
- [1] 뻔히 이산측도 via
discrete measure