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Monotonicity and total boundednessin spaces of measurable functions

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 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.

Pure mathematicslinear continuumMeasurable functionGeneral Mathematics010102 general mathematicsMonotonic function01 natural scienceslinearly ordered set010101 applied mathematicsmodulus of $A$-decreasemeasure of noncompactneLinear continuumSettore MAT/05 - Analisi Matematicamodulus of $A$-increase0101 mathematicsMeasurable functiontotal boundedneMathematics
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