# Monotonicity and total boundednessin spaces of measurable functions

Diana Caponetti, Alessandro Trombetta, Giulio Trombetta

Risultato della ricerca: Article

### 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 $L_0(\Omega)$ of real-valued measurable'' functions defined on a linearly ordered set $\Omega$. We extend the definitions to subsets $X$ of $L_0(\Omega)$, and we use the obtained quantities, $d(X)$ and $i(X)$, to estimate the Hausdorff measure of noncompactness $\gamma(X)$ of $X$. Compactness criteria, in special cases, are obtained.
Lingua originale English 1497-1508 12 Mathematica Slovaca 67 Published - 2017

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Hausdorff Measure of Noncompactness
L-space
Ordered Set
Measurable function
Compactness
Monotonicity
Modulus
Linearly
Subset
Estimate

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cita questo

Monotonicity and total boundednessin spaces of measurable functions. / Caponetti, Diana; Trombetta, Alessandro; Trombetta, Giulio.

In: Mathematica Slovaca, Vol. 67, 2017, pag. 1497-1508.

Risultato della ricerca: Article

Caponetti, D, Trombetta, A & Trombetta, G 2017, 'Monotonicity and total boundednessin spaces of measurable functions', Mathematica Slovaca, vol. 67, pagg. 1497-1508.
Caponetti, Diana ; Trombetta, Alessandro ; Trombetta, Giulio. / Monotonicity and total boundednessin spaces of measurable functions. In: Mathematica Slovaca. 2017 ; Vol. 67. pagg. 1497-1508.
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