Affiliation:
1. Dipartimento di Matematica e Informatica Università di Palermo I-90123 Palermo Italy
2. Dipartimento di Matematica Università della Calabria Arcavacata di Rende Cosenza Italy
Abstract
Abstract
We define and study the moduli d(x, 𝓐, D) and i(x, 𝓐,D) related to monotonicity of a given function x of the space L
0(Ω) of real-valued “measurable” functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L
0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness γ(X) of X. Compactness criteria, in special cases, are obtained.
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