Sequences of events and their limits Flashcards
1
Q
What is an equivalent statement to the following?
A
2
Q
What is the following equal to.
A
3
Q
What is the following equal to?
A
4
Q
What is the following equal to?
A
5
Q
Define lim sup An.
A
6
Q
What is the following equal to?
A
7
Q
What does lim sup An mean in terms of word?
A
Infinitly many of the An’s occur.
8
Q
Define lim inf An.
A
9
Q
What does lim inf An mean in terms of words?
A
The An’s will occur eventually
10
Q
Define lim An.
A
11
Q
Define increaseing/decreasing sequences.
A
12
Q
What is a good way to think of a decreasinf sequence?
A
One that becomes more restrictive
13
Q
Finish the following lemma.
A
14
Q
Prove the following lemma.
A
15
Q
What is Boole’s inequality lemma.
A
16
Q
Prove the following lemma.
A
17
Q
What is the Borel-Cantelli lemma?
A
18
Q
Prove the following lemma.
A
19
Q
A
