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context: i am trying to understand convergence of sequence of random variables.

random variable are just measurable functions but

I still cant get my head around the connection between sequence of functions and sequence of sets. To start suppose [tex]A_n \subset \Omega [/tex] i dont even understand this definition [tex] sup_{k \geq n} A_{k} := \bigcup^{\infty}_{k=n}A_k [/tex].

could someone explain this to me with a concrete example, or point me to a book that deals with sequence of sets and sequence of functions

thanks

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# Limit of sets and functions

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