Prove that if A is a set of positive, finite Lebesgue measure, then almost every point of A is a density point.
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A point x of a measurable subset A of the reals is called a density point if
m( A intersection [x-h, x+h] ) / 2h goes to 1 as h goes to 0
where m is the Lebesgue measure.
Prove that if A is a set of positive, finite Lebesgue measure, then almost every point of A is a density point.
I would like to note that I can use any results from Royden's Real Analysis book.
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