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 L0(Ω) of real-valued "measurable" functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness λ(X) of X. Compactness criteria, in special cases, are obtained.
Monotonicity and total boundedness in spaces of "measurable" functions
Caponetti D.;Trombetta A.;Trombetta G.
2017-01-01
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 L0(Ω) of real-valued "measurable" functions defined on a linearly ordered set Ω. We extend the definitions to subsets X of L0(Ω), and we use the obtained quantities, d(X) and i(X), to estimate the Hausdorff measure of noncompactness λ(X) of X. Compactness criteria, in special cases, are obtained.File in questo prodotto:
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