Monotonicity and total boundedness in spaces of ``measurable'' functions

In: Mathematica Slovaca, vol. 67, no. 6

Diana Caponetti - Alessandro Trombetta - Giulio Trombetta

Detaily:

Rok, strany: 2017, 1497 - 1508

Kľúčové slová:

measurable function, linearly ordered set, modulus of $\A$-decrease, modulus of $\A$-increase, total boundedness, measure of noncompactness, linear continuum

DOI: https://doi.org/10.1515/ms-2017-0065

O článku:

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 $L₀(\Om)$ of real-valued ``measurable'' functions defined on a linearly ordered set $\Om$. We extend the definitions to subsets $X$ of $L₀(\Om)$, 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.

Ako citovať:

ISO 690:

Caponetti, D., Trombetta, A., Trombetta, G. 2017. Monotonicity and total boundedness in spaces of ``measurable'' functions. In Mathematica Slovaca, vol. 67, no.6, pp. 1497-1508. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0065

APA:

Caponetti, D., Trombetta, A., Trombetta, G. (2017). Monotonicity and total boundedness in spaces of ``measurable'' functions. Mathematica Slovaca, 67(6), 1497-1508. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0065

O vydaní:

Publikované: 27. 11. 2017