On extension of a given finitely additive field-valued, non negative measure, on a finitely additive Boolean tribe, to another tribe more ample

Otton Martin Nikodým

Rendiconti del Seminario Matematico della Università di Padova (1956)

  • Volume: 26, page 232-327
  • ISSN: 0041-8994

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Nikodým, Otton Martin. "On extension of a given finitely additive field-valued, non negative measure, on a finitely additive Boolean tribe, to another tribe more ample." Rendiconti del Seminario Matematico della Università di Padova 26 (1956): 232-327. <http://eudml.org/doc/106954>.

@article{Nikodým1956,
author = {Nikodým, Otton Martin},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Differentiation and Integration of Real Functions; Measure Theory},
language = {eng},
pages = {232-327},
publisher = {Seminario Matematico of the University of Padua},
title = {On extension of a given finitely additive field-valued, non negative measure, on a finitely additive Boolean tribe, to another tribe more ample},
url = {http://eudml.org/doc/106954},
volume = {26},
year = {1956},
}

TY - JOUR
AU - Nikodým, Otton Martin
TI - On extension of a given finitely additive field-valued, non negative measure, on a finitely additive Boolean tribe, to another tribe more ample
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1956
PB - Seminario Matematico of the University of Padua
VL - 26
SP - 232
EP - 327
LA - eng
KW - Differentiation and Integration of Real Functions; Measure Theory
UR - http://eudml.org/doc/106954
ER -

References

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  1. (1) S. Banach, Operacje linjouce. Warszawa1931. 
  2. (2) Otton Martin Nikodým, Sur l'extension d'une mesure non Archimédienne simplement additive sur une tribu de Boole simplement additive, à une autre tribu plus étendue: I. Les «bouts» dans une chaîne. Comptes rendus des Séances de l'Académie des Sciences. (Paris), t. 241, (1955), p. 1439-1440. Zbl0065.26404MR73670
  3. II « Agrégats » et leur norm. C. R. (Paris), t. 241, (1955), p. 1544-1545. 
  4. III. Extension de mesure. C. R. (Paris), t. 241, (1955), p. 1695-1696. MR74487
  5. IV. Extension dans les cas general. C. R. (Paris), t. 242, (1956), pag. 864-866. MR75276
  6. (3) Otton Martin Nikodým, Sur les êtres fonctionoïdes. I. Une généralisation de la notion de fonctions. C. R. (Paris), t. 226, (1948), p. 375-377. Zbl0029.22002MR23328
  7. II Procédé de complétion asymptotique. C. R. (Paris), t. 226, (1948), p. 458-460. MR23329
  8. III. Échelle spectrale et intégration des êtres fonctionoïdes. C. R. (Paris), t. 226, (1948), p. 541-543. Zbl0029.22004MR23330
  9. (4) E. Abtin and O. Schreier, Algebraische Konstruction reeller Körper. Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität. V Bd. (1926), p. 85-99. JFM52.0120.05
  10. (5) E. Steinitz, Algebraische Theorie der Körper. Journal fiir die reine und angewandte Mathematik, (1910), Bd. 137, p. 167-309. Zbl41.0445.03JFM41.0445.03
  11. (6) B.L. Van Der Waerden, Moderne Algebra. Reprinted by Frederick Unger Publishing Co.New York, (1943). JFM56.0138.01
  12. (7) B. Russell and N. Whitehead, Principia Mathematicae. Vol. I. Cambridge, (England), (1910). JFM41.0083.02
  13. (8) Otton Martin Nikodým and Stanislawa Nikodým, Sur l'extension des corps algébriques abstraits par un procédé généralisé de Cantor. Rendiconti dell'Accademia Nazionale dei Lincei (Classe di Scienze fisiche, matematiche e naturali). Serie 8, vol. 17, (1954), p. 334-339. Zbl0065.02304MR72123
  14. (9) H. Hahn, Uber die Nichtarchimedischen Grössensysteme. Sitzber. d. Math. Naturwiss. Kl. d. Kais. Akad. d. Wissenschaften. Wien, Vol. 116. Abt. IIa, (1907), p. 601-655. Zbl38.0501.01JFM38.0501.01
  15. (10) Otton Martin Nikodým, Critical remarks on some basic notions in Boolean lattices I. Academia Brasileira de Ciencias, Vol. 24, (1952), p. 113-136. Zbl0047.26303MR49158
  16. (11) Otton Martin Nikodým, Remarks on the Lebesgue's measure extension device for finitely additive Boolean lattices. Proceeding of the National Academy of Sciences, Vol. 37, (1951), p. 533-537. Zbl0044.27701MR43863
  17. (12) G. Birkhoff, Lattice Theory. 2d edition, (1948), New York. [Amer. Math. Soc. Coll. Publ., Vol. 25]. Zbl0033.10103MR29876
  18. (13) H.M. Mac Neille, Pertially ordered sets. Trans. Amer. Math. Soc.. Vol. 42, (1937), p. 416-460. JFM63.0833.04
  19. (14) A. Gleyzal, Transfinite numbers. Proceed. Nat. Acad. Sc. U.S.A., Vol. 23, (1937), p. 281-287. Zbl63.0095.02JFM63.0095.02
  20. (15) C. Carathéodory, Entwurf für eine Algebraisierung des Integralbegriffs. Münch. Sitzungsber., (1938), p. 27-68. JFM64.0189.02
  21. (16) René De Possel, Sur la dérivation abstraite des fonctions d'ensemble. Journ. de Math., t. 101, (1936), p. 391-409. Zbl0015.20505
  22. (17) M.H. Stone, The theory of representation for Boolean algebras. Trans. Amer. Math. Soc., 40, (1936), p. 37-111. Zbl0014.34002MR1501865
  23. (18) J.N. Tukey, Convergence and unifomity in topology. Annals of Mathematics Studies N. 2, Princeton (1940). MR2515JFM66.0961.01

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