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I'm studying the physics of complex systems and I'm approaching probability theory.

I understand that we need a ## \sigma-algebra ## and the Kolmogorov axioms in order to define a probability space but then I bumped into the following relation:

$$ p(A_1 \cup A_2 ) = p( A_1 ) + p( A_2 ) - p( A_1 \cap A_2 ) $$

where ## A_1, A_2 ## are two sets of events that satisfy Kolmogorov axioms. I used all the properties i know to understand it but I wasn't able to demonstrate it. The book says that this equation comes from Kolmogorov axioms...

Can you help me?

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# I A simple question about probability theory

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