For the question 6, i think the Answer C is also correct. Proof: A Δ B=(A-B) ⋃(B-A) and A⋃B= (A-B) ⋃(B-A) ⋃(A⋂B) where (A-B), (B-A) and (A⋂B) are disjoint, Now m*(B) ≤ m*(A⋃B) ≤ m*(A Δ B )+ m*(A⋂B) ≤ m*(A-B) +m*(B-A) +m*(A⋂B) ≤0 + m*(B-A) + 0 ≤ m*(B) Since m*(A⋂B) = 0, then m*(B) = m*(A Δ B ).
For the question 6, i think the Answer C is also correct.
Proof:
A Δ B=(A-B) ⋃(B-A)
and
A⋃B= (A-B) ⋃(B-A) ⋃(A⋂B)
where (A-B), (B-A) and (A⋂B) are disjoint,
Now
m*(B) ≤ m*(A⋃B)
≤ m*(A Δ B )+ m*(A⋂B)
≤ m*(A-B) +m*(B-A) +m*(A⋂B)
≤0 + m*(B-A) + 0 ≤ m*(B)
Since m*(A⋂B) = 0, then m*(B) = m*(A Δ B ).
m*(A intersection B) is 0?
How
Since A ∩ B ⊂ A and m*(A)=0, then
0 ≤ m*(A ∩ B) ≤ m*(A) = 0
Hence, m*(A ∩ B)=0
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OUTSTANDING MIND BLOWING SUPERB
R is measurable Please explain
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Hello Gunnu didi
Please share basic introduction to measure theory concepts also
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