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A note on measures on time scales

Rzeżuchowski T.

Demonstratio Mathematica

2005

Vol. 38, nr 1

79--84

A connection between the measures used on time scales and usual Lebesgue measure is established and applied to simple justifications of some recently published results on Vitali covering theorem and (delta)-differentiability of monotone functions defined on time scales.

Measures of noncompactness related to monotonicity

Banaś J., Olszowy L.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

13-23

We investigate measures of noncompactness related to the monotonicity of functions. Several properties of these measures of non-compactness are derived. Particularly we give the estimates of these measures with help of the Hausdorff distance from the family of nondecreasing or nonincreasing functions. Such a result indicates some connections with approximation theory.