Given a topological space, its Baire sets form the smallest \(\sigma\)-algebra that makes all continuous real-valued functions measurable, its Borel sets form the \(\sigma\)-algebra generated by its topology. In [Czech. Math. J. 7(82), 248--253 (1957; Zbl 0091.05501)] \textit{J. Mařík} proved that in a normal and countably paracompact space every Baire measure admits a unique regular Borel extension. Thus, Dowker spaces (normal but \textit{not} countably paracompact) are spaces where such an extension theorem may fail. \textit{P.~Simon} [Commentat. Math. Univ. Carol. 12, 825--834 (1971; Zbl 0232.54026)] proved that \textit{M.~E. Rudin}'s Dowker space [Fundam. Math. 73, 179-186 (1971; Zbl 0224.54019)] does not have Mařík's extension property. Rudin's space is a subspace of the box product \(\prod_{n<\omega}\omega_{n+2}\), where each factor carries its order topology. The authors investigate a class of spaces, which they call Rudin spaces, these are closed subspaces of Rudin's space~\(X\) that are cofinal in \(X\cap\prod_{n<\omega}g(n)\) with respect to the product order, for some ordinal valued function~\(g\) (that varies with the subspace). One such example is \textit{M. Kojman} and \textit{S. Shelah}'s Dowker subspace of~\(X\) of cardinality~\(\aleph_{\omega+1}\) from [Proc. Am. Math. Soc. 126, No.8, 2459-2465 (1998; Zbl 0895.54022)]. They prove that no Rudin space satisfies Mařík's theorem but that in many Rudin spaces of cardinality~\(\aleph_{\omega+1}\) every Baire measure has some Borel extension. If the latter fails for at least one Rudin space then the continuum must be real-valued measurable.