Monotonicity and total boundednessin spaces of measurable functions

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