측도,measure

QQQ
잰다(measure) = 측정(measurement)한다 = 크기(size)를 부여한다 ?

MKL
해석학,analysis
측정,measurement
노름,norm
정확도,accuracy
정밀도,precision
재현율,recall
가측성,measurability
가측집합,measurable_set - 가측성을 가진 집합,set? chk
측도론,measure_theory
크기,size
길이,length
시그마대수,sigma-algebra ... 가측집합,measurable_sets을 모아 놓은? chk
측도공간,measure_space - w, rr
{
측도,measure가 부여된 가측공간,measurable_space? chk

측도공간 중에서, 전체 측도가 1이면 확률공간,probability_space? chk

Sub
완비측도공간,complete_measure_space - 완비성,completeness

} // measure space ...

측도공간 ...(

측도공간 x 2024-04)

가측공간,measurable_space - writing
{
MKL
시그마대수,sigma-algebra

Up: 가측성,measurability 공간,space
Cmp: 가측집합,measurable_set

} // measurable space ...

measurable space

metric - 비교 필요 ... //

metric
양,quantity
넓이,area를 구한다는 것이
적분,integration이므로 measure와 밀접
확률,probability
확률론,probability_theory
영,zero vs 널,null / 원점,origin
절대값,absolute_value

Contents

1. F측도 F measure = F score
2. F1 측도 F1 measure = F1 score
3. Borel measure
4. Lebesgue measure
5. 완비측도 complete measure
6. 셈 측도 counting measure
7. 이산측도 discrete measure
8. 디랙 측도 Dirac measure
9. 절대 연속 측도 absolutely continuous measure
10. 불변측도 invariant measure
11. 측도추가 ADDHERE
12. 측도추가 ADDHERE
13. 측도추가 ADDHERE

1. F측도 F measure = F score ¶

2. F1 측도 F1 measure = F1 score ¶

Harmonic mean of precision and recall.
정밀도,precision와 재현율,recall의 조화평균,harmonic_mean.

F1 = 2 * (precision * recall) / (precision + recall)

$F_1=\frac{2}{\frac1{\rm Precision}+\frac1{\rm Recall}}$

Sources:
Kwak Slides 1 p74
https://www.ibm.com/docs/en/cloud-paks/cp-data/4.6.x?topic=overview-f1-measure

3. Borel measure ¶

보렐_측도,Borel_measure
https://mathworld.wolfram.com/BorelMeasure.html
https://encyclopediaofmath.org/wiki/Borel_measure
...

5. 완비측도 complete measure ¶

완비측도,complete_measure

Sub:
르베그_측도,Lebesgue_measure

MKLINK
완비측도공간,complete_measure_space

tmp see https://ko.wikipedia.org/wiki/완비_측도_공간

https://encyclopediaofmath.org/wiki/Complete_measure

6. 셈 측도 counting measure ¶

셈측도,counting_measure
{ (tmp copy; update local, DONOTMODIFYHERE)
/// from [https]

[https]

수학백과: 측도 30% 쯤 "보기 1"
공집합,empty_set이 아닌 집합 $X$ 에 대해
$X$ 의 멱집합,power_set을 $\mathcal{M}$ 이라 하면 시그마대수,sigma-algebra가 됨.
부분집합,subset $A\subset X$ 에 대해
$\mu(A)$ 를 $A$ 의 원소의 개수(기수,cardinal_number, 카디널리티,cardinality)로 정의하면,
$\mu$ 는 측도,measure이며 이를 셈측도(counting measure)라 함.

counting_measure
https://planetmath.org/CountingMeasure

Counting_measure

셈측도
https://proofwiki.org/wiki/Definition:Counting_Measure
}

7. 이산측도 discrete measure ¶

이산측도,discrete_measure w

Discrete_measure

8. 디랙 측도 Dirac measure ¶

디랙_측도,Dirac_measure w

9. 절대 연속 측도 absolutely continuous measure ¶

absolutely continuous measure
절대연속측도,absolutely continuous measure

절대연속성,absolute_continuity w
{
absolute continuity n.
absolutely continuous adj.

https://mathworld.wolfram.com/AbsolutelyContinuous.html

Up: absoluteness? {

absoluteness } 연속성,continuity
}
측도,measure

absolutely continuous measure

absolutely continuous measure { 2024-01-27 absolutely continuous measure 절대연속측도 }

10. 불변측도 invariant measure ¶

불변측도,invariant_measure w

quasi-invariant measure는 뭐로 번역? tbd.

11. 측도추가 ADDHERE ¶

12. 측도추가 ADDHERE ¶

13. 측도추가 ADDHERE ¶

https://mathworld.wolfram.com/Measure.html

Measure_(mathematics)
https://encyclopediaofmath.org/wiki/Measure

[https]

수학백과: 측도

[https]

https://en.citizendium.org/wiki/Measure_(mathematics)

측도론,measure_theory