Publication date
May 1996
DOI Publisher
Academic Press. ISSN
0022-247X Citation count (estimate)
1Abstract
AbstractOne of the results reads as follows. Let (ΩΣ,μ) be a measure space with at least two disjoint sets of finite and positive measure. Suppose thatm,φ,ψ:(0,∞)→(0,∞) are functions such that φ and ψ are bijective, and φ(1)=1=ψ(1). Then[formula]for all nonnegative simple functionsx:Ω→R,x≢0 μ-a.e., and allt<0, where Ω(x)≔{ω∈Ω:x(ω)≠0}, if, and only if,m,φ,ψ are multiplicative and ψ=m∘φ−1. If, moreover, arbitrary two functions chosen from the set {m,φ,ψ} satisfy some modest regularity assumptions then the homogeneity relation (∗) holds true if, and only if,m, φ, and ψ are the power functions
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