We define and study the moduli d(x, , D) and i(x, ,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 γ(X) of X. Compactness criteria, in special cases, are obtained
Caponetti, D., Trombetta, A., Trombetta, G. (2017). Monotonicity and total boundednessin spaces of measurable functions. MATHEMATICA SLOVACA, 67(6), 1497-1508 [10.1515/ms-2017-0065].
Monotonicity and total boundednessin spaces of measurable functions
D. Caponetti;
2017-01-01
Abstract
We define and study the moduli d(x, , D) and i(x, ,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 γ(X) of X. Compactness criteria, in special cases, are obtained
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