Construction of a separately continuous function with given oscillation - Maslyuchenko, V. K.; Maslyuchenko, O. V.; Маслюченко, В. К.; Маслюченко, О. В. (Institute of Mathematics, NAS of Ukraine, 1998)
We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support can be covered by countably many sets, which are locally contained in products of sets of the first category.