MHB What is the concept of limiting event?

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Would any member of math help board prove highlighted 1 and 2 by simple and clear explanation with examples?
 
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These are definitions, there is nothing to prove.
 
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WMDhamnekar said:
with examples?

Try letting ##E_k## be the set defined by the open interval ##( 1 - \frac{1}{2^k} , 2 + \frac{1}{2^k})##
 

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