Euler integration over definable functions

Yuliy Baryshnikova, Robert Ghristb

Research output: Contribution to journalArticlepeer-review


We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks.

Original languageEnglish (US)
Pages (from-to)9525-9530
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number21
StatePublished - May 25 2010
Externally publishedYes


  • Definable functions
  • Euler characteristic
  • O-minimal structures
  • Sensor network

ASJC Scopus subject areas

  • General

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