E'lir Kramer
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I am reading http://walrandpc.eecs.berkeley.edu/126notes.pdf on the theory of random processes. The authors are making use of some unfamiliar notation early on, and I don't want to move on without understanding their formalisms.
First one is the := operator and a union operator that looks like it's being used as a variable.
From the text, section 2.3:
"We want to be able to say that if the events A_{n} for n = 1,2,..., are such that A_{n} \subset A_{n+1} for all n and if A:=\bigcup _{n}A_{n}, then P(A_{n}) \uparrow P(A) as n \rightarrow \infty."
What does A:=\bigcup _{n}A_{n} mean? How do you pronounce that phrase in English?
What does the up arrow mean in the next phrase? Is this a strange way of expressing "the limit of P(A_{n}) as n goes to infinity is P(A)? (Which makes sense in context).
First one is the := operator and a union operator that looks like it's being used as a variable.
From the text, section 2.3:
"We want to be able to say that if the events A_{n} for n = 1,2,..., are such that A_{n} \subset A_{n+1} for all n and if A:=\bigcup _{n}A_{n}, then P(A_{n}) \uparrow P(A) as n \rightarrow \infty."
What does A:=\bigcup _{n}A_{n} mean? How do you pronounce that phrase in English?
What does the up arrow mean in the next phrase? Is this a strange way of expressing "the limit of P(A_{n}) as n goes to infinity is P(A)? (Which makes sense in context).