@MISC{SRINGS_1.MIZ,
  AUTHOR = {Coghetto, Roland},
  TITLE = {Semiring of Sets},
  DAY = {31},
  MONTH = {March},
  YEAR = {2014},
  SECTION1 = {Preliminaries},
  SECTION2 = {The Existence of Partitions},
  SECTION3 = {Partitions in a Difference of Sets},
  SECTION4 = {Countable Covers},
  ADDRESS1 = {Rue de la Brasserie 5\\7100 La Louvi\`ere\\Belgium},
  SUMMARY = {Schmets \cite{Schmets:2004} has developed a measure
  theory from a generalized notion of a semiring of sets.
  Goguadze \cite{GOGUADZE:2003} has introduced another generalized
  notion of semiring of sets and prove that all know properties that
  semiring have according to the old definitions are preserved.
  We show that this two notions are almost equivalent.
  We note that Patriota \cite{2011arXiv1103.6166P} told these
  quasi-semi-ring. We propose the formalization of some properties
  developed by the authors.}}

@BOOKLET{Schmets:2004,
TITLE = {Th\´eorie de la mesure},
AUTHOR = {Schmets,Jean},
HOWPUBLISHED = {Notes de cours, Universit\'e de Li\`ege, 146 pages},
YEAR = {2004},
LANGUAGE={French},
PAGES={1-4},
PDF = {http://www.anmath.ulg.ac.be/js/ens/tm.pdf},
URL = {http://www.anmath.ulg.ac.be/js/ens.html}
}

@ARTICLE{GOGUADZE:2003,
year={2003},
issn={0001-4346},
journal={Mathematical Notes},
volume={74},
issue={3-4},
doi={10.1023/A:1026102701631},
title={About the Notion of Semiring of Sets},
url={http://dx.doi.org/10.1023/A%3A1026102701631},
publisher={Kluwer Academic Publishers-Plenum Publishers},
keywords={semiring; partition of a set; continuation of a partition; multiplicative class of sets; product of partitions},
author={Goguadze, D.F.},
pages={346-351},
language={English}
}

@ARTICLE{2011arXiv1103.6166P,
   author = {{Patriota}, A.~G},
    title = {A note on Carath$\backslash$'eodory's Extension Theorem},
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1103.6166},
 primaryClass = "math.PR",
 keywords = {Mathematics - Probability},
     year = 2011,
    month = mar,
   adsurl = {http://adsabs.harvard.edu/abs/2011arXiv1103.6166P},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
