Lebesgue'i välismõõt

olemus
reaalarvude hulgas $$\mathbb{R}$$
lahtiste lõikude $$(a_i,b_i) =\{ r\in\mathbb{R}\colon a_i < r < b_i\}$$
abil defineeritud välismõõt

$$\lambda(A)= \inf_{\mathscr{C}}\limits\{\sum_{i=1}^\infty(b_i-a_i)\colon \mathscr{C}=\{(a_i,b_i)\}_{i\in\mathbb{N}}\;, \; A\subseteq \cup_{i=1}^\infty (a_i, b_i)\}$$

st $$\lambda(A)$$ on hulga $$A$$ kõikvõimalike loenduvate
lahtistest lõikudest koosnevate katete $$\mathscr{C}$$
summaarsete pikkuste alaraja
=
the outer measure that is defined in the set of real numbers by means of open segments

ülevaateid
https://math.stackexchange.com/questions/26676/what-is-the-difference-between-outer-measure-and-lebesgue-measure

https://www.kuk.ac.in/userfiles/file/distance_education/Year-2011-2012/Lecture-5%20(Paper%201).pdf

http://mathonline.wikidot.com/the-lebesgue-outer-measure

http://math.gmu.edu/~dwalnut/teach/Math776/Spring11/776s11lec03_notes.pdf

https://faculty.etsu.edu/gardnerr/5210/notes/2-2.pdf

https://web.ma.utexas.edu/users/drp/files/Fall2020Projects/[Keith,%20Michael]%20An%20Intuitive%20Guide%20to%20Lebesgue%20Measure20201207%20-%20Michael%20Keith.pdf

vt ka
- Lebesgue'i mõõt

Lebesgue'i välismõõt

olemus
reaalarvude hulgas $$\mathbb{R}$$
lahtiste lõikude $$(a_i,b_i) =\{ r\in\mathbb{R}\colon a_i < r < b_i\}$$
abil defineeritud välismõõt

$$\lambda(A)= \inf_{\mathscr{C}}\limits\{\sum_{i=1}^\infty(b_i-a_i)\colon \mathscr{C}=\{(a_i,b_i)\}_{i\in\mathbb{N}}\;, \; A\subseteq \cup_{i=1}^\infty (a_i, b_i)\}$$

st $$\lambda(A)$$ on hulga $$A$$ kõikvõimalike loenduvate
lahtistest lõikudest koosnevate katete $$\mathscr{C}$$
summaarsete pikkuste alaraja
=
the outer measure that is defined in the set of real numbers by means of open segments

ülevaateid
https://math.stackexchange.com/questions/26676/what-is-the-difference-between-outer-measure-and-lebesgue-measure

https://www.kuk.ac.in/userfiles/file/distance_education/Year-2011-2012/Lecture-5%20(Paper%201).pdf

http://mathonline.wikidot.com/the-lebesgue-outer-measure

http://math.gmu.edu/~dwalnut/teach/Math776/Spring11/776s11lec03_notes.pdf

https://faculty.etsu.edu/gardnerr/5210/notes/2-2.pdf

https://web.ma.utexas.edu/users/drp/files/Fall2020Projects/[Keith,%20Michael]%20An%20Intuitive%20Guide%20to%20Lebesgue%20Measure20201207%20-%20Michael%20Keith.pdf

vt ka
- Lebesgue'i mõõt

Palun oodake...

Lebesgue'i välismõõt

olemus
reaalarvude hulgas $$\mathbb{R}$$
lahtiste lõikude $$(a_i,b_i) =\{ r\in\mathbb{R}\colon a_i < r < b_i\}$$
abil defineeritud välismõõt

$$\lambda(A)= \inf_{\mathscr{C}}\limits\{\sum_{i=1}^\infty(b_i-a_i)\colon \mathscr{C}=\{(a_i,b_i)\}_{i\in\mathbb{N}}\;, \; A\subseteq \cup_{i=1}^\infty (a_i, b_i)\}$$

st $$\lambda(A)$$ on hulga $$A$$ kõikvõimalike loenduvate
lahtistest lõikudest koosnevate katete $$\mathscr{C}$$
summaarsete pikkuste alaraja
=
the outer measure that is defined in the set of real numbers by means of open segments

ülevaateid
https://math.stackexchange.com/questions/26676/what-is-the-difference-between-outer-measure-and-lebesgue-measure

https://www.kuk.ac.in/userfiles/file/distance_education/Year-2011-2012/Lecture-5%20(Paper%201).pdf

http://mathonline.wikidot.com/the-lebesgue-outer-measure

http://math.gmu.edu/~dwalnut/teach/Math776/Spring11/776s11lec03_notes.pdf

https://faculty.etsu.edu/gardnerr/5210/notes/2-2.pdf

https://web.ma.utexas.edu/users/drp/files/Fall2020Projects/[Keith,%20Michael]%20An%20Intuitive%20Guide%20to%20Lebesgue%20Measure20201207%20-%20Michael%20Keith.pdf

vt ka
- Lebesgue'i mõõt

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