Let $\mathcal{H}^n$ denote the Hausdorff measure, $\dim_H X$ the Hausdorff dimension, and $\dim X$ the topological dimension of $X$.

A well known result of Szpilrajn (He changed his name to Marczewski while hiding from Nazi persecution) proved in [S] asserts that if $\mathcal{H}^{n+1}(X)=0$, then the topological dimension of $X$ is at most $n$.

Szpilrajn's proof is reproduced in [Theorem 7.3, HW] and [Theorem 8.15, H].

Szpilrajn however, mentions in [S] that his argument is based Nobeling's proof of a weaker result that topological dimension is bounded from above by the Hausdorff dimension of a metric space. However, he did not provide any reference to Nobeling's work.

There is also no reference to Nobeling's work in the book by Hurewicz and Wallman.

Question. Does anybody know the reference to the original work of Nobeling?

[H] J. Heinonen, Lectures on analysis on metric spaces. Universitext. Springer-Verlag, New York, 2001.

[HW] W. Hurewicz, H. Wallman, Dimension Theory. Princeton Mathematical Series, v. 4. Princeton University Press, Princeton, N. J., 1941.

[S] E. Szpilrajn, La dimension et la mesure, Fund. Math. 28 (1937), 81--89.