The reverse mathematics of theorems of jordan and lebesgue

Andre Nies, Marcus A. Triplett, Keita Yokoyama

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The Jordan decomposition theorem states that every function of bounded variation can be written as the difference of two non-decreasing functions. Combining this fact with a result of Lebesgue, every function of bounded variation is differentiable almost everywhere in the sense of Lebesgue measure. We analyze the strength of these theorems in the setting of reverse mathematics. Over, a stronger version of Jordan's result where all functions are continuous is equivalent to, while the version stated is equivalent to. The result that every function on of bounded variation is almost everywhere differentiable is equivalent to. To state this equivalence in a meaningful way, we develop a theory of Martin-Lof randomness over.

Original languageEnglish
Pages (from-to)1657-1675
Number of pages19
JournalJournal of Symbolic Logic
Issue number4
Publication statusPublished - 2021 Dec 1

ASJC Scopus subject areas

  • Philosophy
  • Logic


Dive into the research topics of 'The reverse mathematics of theorems of jordan and lebesgue'. Together they form a unique fingerprint.

Cite this