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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 Lebesgue measurable ones

Morayne M., Ryll-Nardzewski C.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 3

263-265

We determine when for a function f : [0, 1] --> R there exist a 1-1 mapping fi of [0, 1] onto [0, 1] and a Lebesgue (Baire) measurable function g : [0, 1] --> R such that f = g o fi.