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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

Open Access
|Aug 2014

References

  1. [1] APPELL, J.-D’ANIELLO, E.-VATH, M.: Some remarks on small sets, Ric. Mat. 50 (2001), 255-274.
  2. [2] GER, R.-KUCZMA, M.: On the boundedness and continuity of convex functions and additive functions, Aequationes Math. 4 (1970), 157-162.10.1007/BF01817756
  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. 325-344.10.18778/7525-971-1.20
  4. [4] KARASIŃSKA,A.-WAGNER-BOJAKOWSKA,E.:Homeomorphisms of linear and planar sets of the first category into microscopic sets, Topology Appl. 159 (2012), 1894-1898.10.1016/j.topol.2011.11.055
  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.
  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, 2009.10.1007/978-3-7643-8749-5
  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.
  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.
  9. [9] RUZIEWICZ, S.-SIERPIŃSKI, W.: Un théoréme sur les familles de fonctions, Mathematica (Cluj) 7 (1933), 89-91.
  10. [10] SIERPIŃSKI, W.: Sur un ensemble non dénombrable, dont toute image continue est de mesure nulle, Fund. Math. 11 (1928), 302-304.10.4064/fm-11-1-302-303
  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), 12-16.10.4064/fm-24-1-12-16
  12. [12] SIERPIŃSKI, W.: Oeuvres Choisies, T. III, PWN, Warszawa, 1975.
  13. [13] SIERPIŃSKI, W.: Sur la question de la mesurabilité de la base de Hamel, Fund. Math. 1 (1920), 105-111.10.4064/fm-1-1-105-111
  14. [14] SIERPIŃSKI, W.: La base de M. Hamel et la propriété de Baire, Publ. Math. Univ. Beograd 4 (1935), 221-225.
  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. 10.4064/fm-22-1-303-311
DOI: https://doi.org/10.2478/tmmp-2014-0008 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
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: 3 issues per year

© 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.