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I have seen this interesting paragraph on a talk page of the Wikipedia article about Polish mathematician Tomek Bartoszyński:

Tomek's paper "Additivity of measure implies additivity of category, Trans. Amer. Math. Soc., 281(1984), no. 1, 209--213" as the first to show that there is (in ZFC) an asymmetry between measure and category. Before that essentially everybody believed that no such asymmetry exists (cf Oxtoby's book Measure and Category), and in my very personal opinion, Tomek's result shook the world and initiated the research that quickly led to Cichon's diagram, among others.

This paragraph sounds quite intriguing. And it came from a user who definitely knows a lot about set theory, judging by their contributions on Wikipedia.1

Would it be possible to outline some basic information of Bartoszyński's results on measure and category and their importance? (Ideally in a way readable by a non-expert in the field.) Adding some references suitable for somebody who wants to start to learn a bit more about this topic would be appreciated too.


1This was a part of discussion about Bartoszyński notability in the sense in which this word is used on Wikipedia. The above comment was added by the Wikipedia with the username Kope, who is most probably Péter Komjáth, although I am not sure whether he officially confirmed this somewhere. He is also active on MathOverflow (and to a lesser extent on Math.SE).

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