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

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.
Linear continuum
Linearly ordered set
Measurable function
Measure of noncompactness
Modulus of A-decrease
Modulus of A-increase
Total boundedness
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/315090
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