A result of Nymann is extended to show that a positive $\sigma$-finite measure with range an interval is determined by its level sets. An example is given of two finite positive measures with range the same finite union of intervals but with the property that one is determined by its level sets and the other is not.
On the structure of level sets of uniform and Lipschitz quotient mappings from ${\mathbb{R}}^n$ to ${\mathbb{R}}$
Subspaces of $L_p$ that embed into $L_p(μ)$ with $μ$ finite
On linearisation, existence and uniqueness of preduals
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