. Geometrical probability and random points on a hypersphere . Ann. Math. Stat ., 38 : 213 – 220 , 1967 .  O . Devillers , M . Glisse , X . Goaoc , G . Moroz and M . Reitzner . The monotonicity of f -vectors of random polytopes . Electron
Relations between I-approximate Dini derivatives and monotonicity are presented. Next, some generalizations of the Denjoy–Young–Saks Theorem
for I-approximate Dini derivatives of an arbitrary real function are proved.
The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations
of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the