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Lebesgue Outer Measure of Intersection of Two Sets

How do we find the Lebsgue outer measure of below set


Set : drive[DOT]google.com/file/d/1-ZwjDEF8LO5nLPEMHPgx8oNArUDQi19b/view?usp=drivesdk


I know that both of them have Lebesgue outer measure of O, but not sure how to take the lebesgue outer measure of the whole set.
Original post by Ash760
How do we find the Lebsgue outer measure of below set


Set : drive[DOT]google.com/file/d/1-ZwjDEF8LO5nLPEMHPgx8oNArUDQi19b/view?usp=drivesdk


I know that both of them have Lebesgue outer measure of O, but not sure how to take the lebesgue outer measure of the whole set.


Can't necessarily help, but your thread title/description doesn't seem to match your link. What two sets are you refering to?

Untitled.jpg

And if the link is correct, then the LOM is going to depend on which sequence of sets {rn}\{r_n\} is chosen and the value of ϵ\epsilon.
(edited 11 months ago)
Reply 2
Original post by ghostwalker
Can't necessarily help, but your thread title/description doesn't seem to match your link. What two sets are you refering to?

Untitled.jpg

And if the link is correct, then the LBO is going to depend on which sequence of sets {ar}\{a_r\} is chosen and the value of ϵ\epsilon.


B =[0,1]\A =[0,1]^(A^c), which is the intersection of two sets
Original post by Ash760
B =[0,1]\A =[0,1]^(A^c), which is the intersection of two sets


So, your two sets are the closed interval 0 to 1, which would have an LOM of 1 (not 0), and A^C, whose LOM will depends on the sequence of r_n chosen, and on epsilon. (Edit: Note: I'm assuming complement wrt [0,1])

Edit2: Correct abbreviation.
(edited 11 months ago)
Original post by Ash760
How do we find the Lebsgue outer measure of below set


Set : drive[DOT]google.com/file/d/1-ZwjDEF8LO5nLPEMHPgx8oNArUDQi19b/view?usp=drivesdk


I know that both of them have Lebesgue outer measure of O, but not sure how to take the lebesgue outer measure of the whole set.

Are you saying that the measure of A is 0? It definitely is not (and obviously neither is [0,1]'s).
(edited 11 months ago)

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