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Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

1 vote
1 answer
60 views

Does a strictly incresing cumulative distribution function in $[0,1]$ always admit a density? [duplicate]

Consider some strictly increasing cdf $G(x):[0,1]\rightarrow [0,1]$. I know $G$ is almost everywhere differentiable since $G$ is monotonic. Moreover, I know $G(x)$ admits a density if and only if it i …
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  • 21
0 votes
1 answer
38 views

Is the set of probability measures on $[0,1]$ that induces a continuous distribution functio...

I am an student in economics and I am trying to solve a fixed point problem, where the inputs of the function are probability measures. I'm trying to figure out whether the below results are true, but …
djsteve's user avatar
  • 21