My question is simple: which of the two spellings of this famous Polish mathematician’s surname is correct?
His most influential result is proving that a $\sigma$-finite measure that is absolutely continuous with respect to another $\sigma$-finite measure on the same measurable space can be represented by integration of a(n almost unique) measurable function with respect to that other measure. This generalizes an earlier theorem proved by Austrian mathematician Johann Karl August Radon.
The spelling with the diacritic (Nikodým) sometimes appears in texts written in the English language, although the usage seems to be pretty inconsistent. I did a little research and found that the version without the diacritic (Nikodym) actually seems to be more prevalent in Polish sources. I do not speak Polish, but I know that the letter ý does not even feature in the Polish alphabet. (Although it does in the closely related Slavic languages Czech and Slovak—maybe O.M.N. had Czech/Slovak ancestors?)
Based on these findings, I am starting to wonder whether the spelling Nikodým is a hypercorrection in the literature written in languages other than Polish. Any comments would be greatly appreciated, even if merely as speculative as my post.
As an addendum, spellings of both [!] of his given names are apparently also rendered inconsistently (Otton/Otto, Marcin/Martin), but that’s for another discussion.
The original spelling of his name is Otton Marcin Nikodym. He was born in Zabłotów near Kołomyja, which until 1945 belonged to Poland (currently it belongs to Ukraine). Also, you are correct that the letter ý does not even feature in the Polish alphabet.
Other spellings of his name are probably translations of his original Polish name (for example, Marcin is often translated to Martin).