(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 $B$_{\alpha}.
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 $B$_{\alpha} is the sum of two
extendable functions g and h from $B$_{\alpha}.
This answers a question of A. Maliszewski.

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