Historical remarks on equivalence of functions

• Autorzy: Lipecki Z.

Identyfikatory

DOI

10.4064/ba8107-4-2017

• Języki publikacji: EN

Abstrakty

EN

A theorem of E. Szpilrajn (Marczewski) (1936) on equivalent functions is recalled and its relation to subsequent results published by M. Morayne and C. Ryll-Nardzewski (1999) and M. Kysiak (2005) is briefly discussed.

Słowa kluczowe

EN

Polish space; equivalent functions; Lebesgue measurable function; function having the Baire property; Borel measurable function; function satisfying condition (s); Marczewski measurable function

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 1
• Strony: 93--95
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Lipecki Z.

• Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

Bibliografia

• [1] K. P. S. Bhaskara Rao and B. V. Rao, Borel spaces, Dissertationes Math. (Rozprawy Mat.) 190 (1981), 62 pp.
• [2] A. Komisarski, H. Michalewski and P. Milewski, Functions equivalent to Borel measurable ones, Bull. Polish Acad. Sci. Math. 58 (2010), 55–64.
• [3] M. Kysiak, Some remarks on indicatrices of measurable functions, Bull. Polish Acad. Sci. Math. 53 (2005), 281–284.
• [4] M. Morayne and C. Ryll-Nardzewski, Functions equivalent to Lebesgue measurable ones, Bull. Polish Acad. Sci. Math. 47 (1999), 263–265.
• [5] J. C. Morgan II, Point Set Theory, Dekker, New York, 1990.
• [6] E. Szpilrajn (Marczewski), Sur certains invariants de l’opération (A), Fund. Math. 21 (1933), 229–235; reprinted in: E. Marczewski, Collected Mathematical Papers, Inst. Math., Polish Acad. Sci., Warszawa, 1996, 50–56.
• [7] E. Szpilrajn (Marczewski), Sur une classe de fonctions de M. Sierpinski et la classe correspondante d’ensembles, Fund. Math. 24 (1935), 17–34; reprinted in: E. Marczewski, Collected Mathematical Papers, Inst. Math., Polish Acad. Sci., Warszawa, 1996, 92–109.
• [8] E. Szpilrajn (Marczewski), Sur l’équivalence des suites d’ensembles et l’équivalence des fonctions, Fund. Math. 26 (1936), 302–326; Correction, Fund. Math. 27 (1936), 294; reprinted in: E. Marczewski, Collected Mathematical Papers, Inst. Math., Polish Acad. Sci., Warszawa, 1996, 124–148.