Skip to main content
Have a personal or library account? Click to login
On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis Cover

On some Problem of Sierpiński and Ruziewicz Concerning the Superposition of Measurable Functions. Microscopic Hamel Basis

Tatra Mountains Mathematical Publications
Volume 58 (2014): Issue 1 (March 2014)
By:  and    
Open Access
|Aug 2014
References

References

  1. [1] APPELL, J.-D’ANIELLO, E.-VATH, M.: Some remarks on small sets, Ric. Mat. 50 (2001), 255-274.
    Search in Google Scholar
  2. [2] GER, R.-KUCZMA, M.: On the boundedness and continuity of convex functions and additive functions, Aequationes Math. 4 (1970), 157-162.
    Open DOISearch in Google Scholar
  3. [3] HORBACZEWSKA, G.-KARASIŃSKA, A.-WAGNER-BOJAKOWSKA, E.: Properties of the σ-ideal of microscopic sets, Chapter 20 in Traditional and Present-Day Topics in Real Analysis, Łódź University Press, Łódź, 2013, pp. 325-344.
    Open DOISearch in Google Scholar
  4. [4] KARASIŃSKA,A.-WAGNER-BOJAKOWSKA,E.:Homeomorphisms of linear and planar sets of the first category into microscopic sets, Topology Appl. 159 (2012), 1894-1898.
    Open DOISearch in Google Scholar
  5. [5] KARASIŃSKA, A.-POREDA, W.-WAGNER-BOJAKOWSKA, E.: Duality principle for microscopic sets, in: Real Functions, Density Topology and Related Topics (M. Filipczak et al., eds.), Łódź University Press, Łódź, 2011, pp. 83-87.
    Search in Google Scholar
  6. [6] KUCZMA, M.: An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality (2nd ed.), Birkh¨auser, Basel, 2009.
    Open DOISearch in Google Scholar
  7. [7] KUCZMA, M.: On some analogies between measure and category and their applications in the theory of additive functions, Ann. Math. Sil. 1 (1985), 155-162.
    Search in Google Scholar
  8. [8] OXTOBY, J. C.: Measure and Category. A survey of the analogies between topological and measure spaces (2nd ed.), in: Grad. Texts in Math., Vol. 2, Springer-Verlag, New York, 1980.
    Search in Google Scholar
  9. [9] RUZIEWICZ, S.-SIERPIŃSKI, W.: Un théoréme sur les familles de fonctions, Mathematica (Cluj) 7 (1933), 89-91.
    Search in Google Scholar
  10. [10] SIERPIŃSKI, W.: Sur un ensemble non dénombrable, dont toute image continue est de mesure nulle, Fund. Math. 11 (1928), 302-304.
    Open DOISearch in Google Scholar
  11. [11] SIERPIŃSKI, W.: Sur un probléme de M. Ruziewicz concernant les superpositions de functions jouissant de la propriété de Baire, Fund. Math. 24 (1935), 12-16.
    Open DOISearch in Google Scholar
  12. [12] SIERPIŃSKI, W.: Oeuvres Choisies, T. III, PWN, Warszawa, 1975.
    Search in Google Scholar
  13. [13] SIERPIŃSKI, W.: Sur la question de la mesurabilité de la base de Hamel, Fund. Math. 1 (1920), 105-111.
    Open DOISearch in Google Scholar
  14. [14] SIERPIŃSKI, W.: La base de M. Hamel et la propriété de Baire, Publ. Math. Univ. Beograd 4 (1935), 221-225.
    Search in Google Scholar
  15. [15] SZPILRAJN, E.: Remarques sur les fonctions complétement additives d’ensemble et sur les ensembles joissant de la propriété de Baire, Fund. Math. 22 (1934), 303-311.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.2478/tmmp-2014-0008 | Journal eISSN: 1338-9750 (formerly 1210-3195) | Journal ISSN: 1210-3195
Journal RSS Feed
Language: English
Page range: 91 - 99
Submitted on: Nov 28, 2013
Published on: Aug 15, 2014
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
microscopic sets,
nullsets,
sets of the first category,
sets having the Baire property,
Lusin set,
Hamel basis
Related subjects:
Mathematics,
General mathematics

© 2014 Aleksandra Karasińska, Elżbieta Wagner-Bojakowska, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2014): Issue 1 (March 2014)
Previous article
Next article