@MISC{SRINGS_4.MIZ,
  AUTHOR = {Coghetto, Roland},
  TITLE = {Finite Product of Semiring of Sets},
  DAY = {19},
  MONTH = {April},
  YEAR = {2015},
  MSC2010 = {28A05, 03E02, 03F30,3B035},
  KEYWORDS = {sets, set partitions, semiring of sets},
  ADDRESS1 = {Rue de la Brasserie 5\\7100 La Louvi\`ere, Belgium},
  ACKNOWLEDGEMENT = {I would like to thank Artur Korni\l owicz for
  suggestions.},
  SUMMARY = {We formalize that the image of a semiring of sets
  \cite{goguadze2003notion}
  by a injective function is a semiring of sets.
  We offer a non-trivial example of semiring of sets in a topological
  space \cite{Schmets:2004}.
  Finally, we show that the finite product of semiring of sets is a semiring
  of sets \cite{Schmets:2004} and
  that the finite product of classical semiring of sets
  \cite{bogachev2007measure}
  is a classical semiring of sets.
  In this case, we use here the notation of the book of Aliprantis and
  Border \cite{aliprantis2006infinite}.}}

@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={2,75},
PDF = {http://www.anmath.ulg.ac.be/js/ens/tm.pdf},
URL = {http://www.anmath.ulg.ac.be/js/ens.html}}

@article{goguadze2003notion,
  title={About the Notion of Semiring of Sets},
  author={Goguadze, DF},
  journal={Mathematical Notes},
  volume={74},
  number={3},
  pages={346--351},
  year={2003},
  publisher={Springer}}

@book{bogachev2007measure,
  title={Measure theory},
  author={Bogachev, Vladimir Igorevich and Ruas, Maria Aparecida Soares},
  volume={1},
  year={2007},
  publisher={Springer}}

@book{aliprantis2006infinite,
  title={Infinite dimensional analysis},
  author={Aliprantis, Charalambos D and Border, Kim C},
  year={2006},
  publisher={Springer-Verlag, Berlin, Heidelberg}}
