(1) For any countable ordinal number \alpha there exists a Borel measurable function g:R-->R such that g+f is a Darboux function (is almost continuous in the sense of Stallings) for every f in . This solves a problem of J. Ceder.
(2) There is a function g that is universally measurable and has the Baire property in restricted sense such that g+f is Darboux for every Borel measurable function f.
(3) There is g:R-->R such that f+g is extendable for each f:R-->R that is Lebesgue measurable (has the Baire property).
(4) For every countable ordinal number \alpha, each f from is the sum of two extendable functions g and h from . This answers a question of A. Maliszewski.
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