Continuous transforms of a Lebesgue measure
Copyright policy )Continuous transforms of a Lebesgue measure
The following statement is proved: Theorem 1. Let \(K\) be a compact metric space which is the continuous image of \([0,1]\) and \(\mu\) be a Borel probability measure on \(K\) whose topological support coincides with \(K\). Then there exists a continuous surjective \(g:[0,1]\to K\) such that \(\lambda\circ g^{-1}=\mu,\) where \(\lambda\) is the Lebesgue measure on \([0,1].\)
- Lomonosov Moscow State University Russian Federation
Probability measures on topological spaces, image of a measure, Lebesgue measure, continuous transform, compact metric space, Set functions and measures on topological spaces (regularity of measures, etc.)
Probability measures on topological spaces, image of a measure, Lebesgue measure, continuous transform, compact metric space, Set functions and measures on topological spaces (regularity of measures, etc.)
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