6533b860fe1ef96bd12c3c10
RESEARCH PRODUCT
Monotonicity and total boundednessin spaces of measurable functions
G. TrombettaAlessandro TrombettaDiana Caponettisubject
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 boundedneMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-11-01 |