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In this short paper the discussion of the pointwise characterization offunctions $f$ in the Sobolev space $W^{m,p}(\R^n)$ given in the recent paper(Bojarski) is supplemented in \SS1 by a direct, essentially geometric, proof ofthe novel inequality (for $m>1$), appearing in Bojarski apparently for thefirst time, and involving the use of the $m$-th difference of the function $f$.  Moreover in \SS2 some additional comments to the text in Bojarski are givenand a natural class of Sobolev spaces in domains $G$ in $\R^n$ is defined. \SS3contains some final remarks.

Sobolev spaces and Lagrange interpolation