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Historical remarks on equivalence of functions

Lipecki Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2017

Vol. 65, no. 1

93--95

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.

Functions equivalent to Borel measurable ones

Komisarski A., Michalewski H., Milewski P.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 1

55-64

Let X and Y be two Polish spaces. Functions ƒ, g : X → Y are called equivalent if there exists a bijection φ from X onto itself such that g º φ = ƒ. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.