Interpolation of Level Sets for Equimeasurable Functions


AbstractThe author proves a new theoretical property for the family of rearrangementsR(f) of a given measurable functionf. Given a finite number of equimeasurable functionsf1,…,fn∈R(f), it is possible to construct a family of equimeasurable functions (ηλ)λ∈[0,1]⊂R(f) which interpolates the functionsf1,…,fnin a convexlike way. However, as an application, this interpolation result yields a compact fixed point property

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Elsevier - Publisher Connector

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