In a measure space (X, A, μ) , we consider two measurable functions f, g: E→ R, for some E∈ A. We prove that the property of having equal p-norms when p varies in some infinite set P⊆ [ 1 , + ∞) is equivalent to the following condition: μ(x∈E:|f(x)|>α)=μ(x∈E:|g(x)|>α)for allα≥0.
On functions having coincident p-norms / Klun, G.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:3(2020), pp. 955-968. [10.1007/s10231-019-00907-z]
On functions having coincident p-norms
Klun G.
2020-01-01
Abstract
In a measure space (X, A, μ) , we consider two measurable functions f, g: E→ R, for some E∈ A. We prove that the property of having equal p-norms when p varies in some infinite set P⊆ [ 1 , + ∞) is equivalent to the following condition: μ(x∈E:|f(x)|>α)=μ(x∈E:|g(x)|>α)for allα≥0.File in questo prodotto:
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Klun_revised 01_07_19.pdf
Open Access dal 21/09/2020
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