The Hahn and Jordan Decomposition Theorems

 

Title: The Hahn and Jordan Decomposition Theorems
Authors: Marie Cousin (marie /dot/ cousin /at/ grenoble-inp /dot/ org), Mnacho Echenim (mnacho /dot/ echenim /at/ univ-grenoble-alpes /dot/ fr) and Hervé Guiol (herve /dot/ guiol /at/ univ-grenoble-alpes /dot/ fr)
Submission date: 2021-11-19
Abstract: In this work we formalize the Hahn decomposition theorem for signed measures, namely that any measure space for a signed measure can be decomposed into a positive and a negative set, where every measurable subset of the positive one has a positive measure, and every measurable subset of the negative one has a negative measure. We also formalize the Jordan decomposition theorem as a corollary, which states that the signed measure under consideration admits a unique decomposition into a difference of two positive measures, at least one of which is finite.
BibTeX:
@article{Hahn_Jordan_Decomposition-AFP,
  author  = {Marie Cousin and Mnacho Echenim and Hervé Guiol},
  title   = {The Hahn and Jordan Decomposition Theorems},
  journal = {Archive of Formal Proofs},
  month   = nov,
  year    = 2021,
  note    = {\url{https://isa-afp.org/entries/Hahn_Jordan_Decomposition.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License