MHB I don't understand the question.

AI Thread Summary
The discussion centers on a question regarding a mathematical expression from Vladimir Bogachev's Measure Theory. The user initially struggles to understand the relationship between the sets E and X-E, believing their interpretation is correct based on De-Morgan's laws. They express confusion over the inclusion of an additional term in their calculation. Ultimately, the user resolves their confusion, realizing that the disjoint nature of sets S, A, and B clarifies the expression. The conversation highlights the challenges of understanding complex mathematical concepts and the importance of careful analysis.
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This is a simple question.

On pages 5-6 of Measure Theory,Vol 1, Vladimir Bogachev he writes that:

for E=(A\cap S)\cup (B\cap (X-S))

Now, he writes that:

X-E = ((X-A)\cap S) \cup ((X-B)\cap (X-S))

But I don't get this expression, I get another term of ((X-B)\cap (X-A))

i.e, X-E =( ((X-A)\cap S) \cup ((X-B)\cap (X-S)))\cup ((X-B)\cap (X-A)).

I believe I did it correctly according to De-Morgan rules and distribution.

I am puzzled...:confused:
 
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Re: Something in Measure Theory.

Nevermind, I got it.

It follows from the fact that S is disjoint to A and B.

Sometimes I wonder how I still can do math...:-D
 

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