sequence of sets convergence
Let {An}∞n=1 be a sequence of sets, and A a set.
The sequence {An}∞n=1 is said to from below to A, (shortly, An↑A or An↗A), iff
1) An⊆An+1 ∀n≥1
2) A=∞⋃n=1An
The sequence {An}∞n=1 is said to from above to A, (shortly, An↓A or An↘A), iff
1) An+1⊆An ∀n≥1
2) A=∞⋂n=1An
In both cases the less accurate notation
A=lim |
is also used.
Title | sequence of sets convergence |
---|---|
Canonical name | SequenceOfSetsConvergence |
Date of creation | 2013-03-22 16:15:12 |
Last modified on | 2013-03-22 16:15:12 |
Owner | Andrea Ambrosio (7332) |
Last modified by | Andrea Ambrosio (7332) |
Numerical id | 8 |
Author | Andrea Ambrosio (7332) |
Entry type | Definition |
Classification | msc 28A05 |