A paper by Grabisch et al (2011) states that the arithmetic and geometric means are Lagrangian means whereas the harmonic mean is not Lagrangian.
What does this mean? What properties does a Lagrangian mean have and what properties do non-Lagrangian means have?
- Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap. Aggregation functions: Means. Information Sciences, Elsevier, 2011, 181 (1), pp.1-22. <10.1016/j.ins.2010.08.043>.