Sequences of events and their limits Flashcards

1
Q

What is an equivalent statement to the following?

A
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2
Q

What is the following equal to.

A
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3
Q

What is the following equal to?

A
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4
Q

What is the following equal to?

A
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5
Q

Define lim sup An.

A
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6
Q

What is the following equal to?

A
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7
Q

What does lim sup An mean in terms of word?

A

Infinitly many of the An’s occur.

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8
Q

Define lim inf An.

A
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9
Q

What does lim inf An mean in terms of words?

A

The An’s will occur eventually

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10
Q

Define lim An.

A
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11
Q

Define increaseing/decreasing sequences.

A
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12
Q

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

A

One that becomes more restrictive

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13
Q

Finish the following lemma.

A
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14
Q

Prove the following lemma.

A
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15
Q

What is Boole’s inequality lemma.

A
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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