Recent content by hj2000

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    Graduate How Does a Non-Atomic Measure Relate to Lebesgue Measure Through a Function?

    if m(.) is a non-atomic measure on the Borel sigma-algebra B(I). I is some fixed closed finite interval in R. How to show that f satisfies the following: m(S) = L(f(S)), S in B(I) where L is the Lebesgue measure and f(x) = m( I intersect(-infinity,x] )
    • hj2000
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    • Measure Measure theory Theory
    • Replies: 1
    • Forum: Calculus
  2. H

    Graduate Density of [0,1]-C on Thick Cantor Set Construction | Sequence {a_n}

    Let C be the thick Cantor set. let {a_n} be a sequence of positive numbers. In the construction of the thick Cantor set, at the n-th stage we remove the middle a_n part of each interval (instead of the middle third as in the ordinary Cantor set). I actually wanted to show that [0,1]-C is...