Monotonicity and total boundednessin spaces of measurable functions
| Autor: | G. Trombetta, Alessandro Trombetta, Diana Caponetti |
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| Přispěvatelé: | Caponetti, D., Trombetta, A., Trombetta, G. |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
linear continuum Measurable function General Mathematics 010102 general mathematics Monotonic function 01 natural sciences linearly ordered set 010101 applied mathematics modulus of $A$-decrease measure of noncompactne Linear continuum Settore MAT/05 - Analisi Matematica modulus of $A$-increase 0101 mathematics total boundedne Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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