Continuity and Outer Measure
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Let f(x) be a positive continuous function on [0,1/2], f(x) =< 1/2.
Let A = { (x,y) : 0 =< x = 1/2, 0=<y=< f(x)}
Prove that; m*(A) = integral from 0 to 1/2 of f(x)dx.
Please I don't want a solution from a book, I want a simple proof based on basic definitionsand given info.
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Continuity and outer measurability are investigated. The solution is detailed and well presented.
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Let be a positive continuous function on and .
Prove that
Proof:
We consider a division of the interval . , where for all . In ...
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