Thomson B.S. Derivates of Interval Functions

Providence: American Mathematical Societu, 1991. — 96 p.Covering relations
Basic language of covering relations
Full and fine covering
Covering lemmas
The variation
Variation of an interval–point function
Differential equivalence
Variational measures
Increasing sets property
Regularity properties
The upper integral
The variational measure as an integral
The fine variational measure as an integral
Differential equivalence
A density theorem
Derivates
Definitions of the derivates
Baire class of derivates
Variational estimates
Lipschitz conditions
Exact derivatives
Absolute continuity and singularity
Basic Definitions
Further properties
Measure properties
A stronger orthogonality relation
Derivation properties and singularity
Characterization of singularity
Derivation properties and absolute continuity
Characterization of absolute continuity
Measures
Lebesgue measure
Total variation measures
Hausdorff measure
Density theorems
Hausdorff dimension
Real functions
Monotonic functions
Functions having σ…finite variation
Absolute continuity and singularity
s–absolute continuity
s–singular functions