  Recently Tomasz Natkaniec in [On lineability of families of non-measurable
functions of two variable. Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat.
RACSAM, 115(1):Paper No. 33, 10, 2021] studied the lineability problem for
several classes of non-measurable functions in two variables. In this note we
improve his results in the direction of algebrability. In particular, we show
that most of the classes considered by Natkaniec contain free algebras with
$2^{\mathfrak{c}}$ many generators.
