https://hal-mines-paristech.archives-ouvertes.fr/hal-01255512de La Fortelle, ArnaudArnaudde La FortelleCAOR - Centre de Robotique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresA study on generalized inverses and increasing functions Part I: generalized inversesHAL CCSD2015[MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA][MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]de La Fortelle, Arnaud2016-01-13 18:17:082022-10-22 05:11:532019-01-28 10:59:02enPreprints, Working Papers, ...application/force-download1Generalized inverses of increasing functions are used in several domains such as function analysis, measure theory, probability and fuzzy logic. Several definitions of the generalized inverse are known leading to different properties. This paper aims at giving a precise study of the link between the definitions and the properties. It is shown why the right-continuous generalized inverse is a good choice. This rigorous treatment opens the doors to more focused studies.