Borel Sigma Algebra generated by Open Intervals Exercises

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One measure theory question.I want to test your knowledge about measure theory. You can have a try.And the formal measure theory task will be held on June 03 .Please write the answer in a clear way. Because your handwriting is hard for me to recognize somtimes.

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Question 1.
(1.1) State the definition of a probability space (2, F,P).
[3 marks]
(1.2) Show that P(lim inf na An) < lim inf n–– P(An) for An EF with n>1.
[3 marks]
(1.3) Let P1 and P, be two probability measures on (R, B(R)) such
that P.((-0, a)) = P2((-0, a)) for all a € Q. Stating clearly
any result to which you appeal, show that P1 = P2 on B(R).
[4 marks)

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Tags:
open intervals

Probability measure

Probability space

the borel sigma

sigma algebra

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