Flashcards in Sequences of events and their limits Deck (19)

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1

What is an equivalent statement to the following?

2

What is the following equal to.

3

What is the following equal to?

4

What is the following equal to?

5

Define **lim sup A _{n}.**

6

What is the following equal to?

7

What does lim sup A_{n} mean in terms of word?

Infinitly many of the A_{n}'s occur.

8

Define **lim inf A _{n}.**

9

What does lim inf A_{n} mean in terms of words?

The A_{n}'s will occur eventually

10

Define** lim A _{n.}**

11

Define **increaseing/decreasing** sequences.

12

What is a good way to think of a decreasinf sequence?

One that becomes more restrictive

13

Finish the following lemma.

14

Prove the following lemma.

15

What is Boole's inequality lemma.

16

Prove the following lemma.

17

What is the Borel-Cantelli lemma?

18

Prove the following lemma.

19