Tarski–Kuratowski theorem

The Tarski–Kuratowski theorem addresses the relationship between different ways of measuring the size of a set, specifically the measure and the category (size in terms of "large" or "small" sets). It states that in certain mathematical spaces, a set is "null" (measure zero) if and only if it is "meager" (category small or "first category"). This theorem connects two concepts used to describe the "smallness" of sets and shows that, under specific conditions, these notions coincide, enriching our understanding of the structure and properties of sets within real analysis and topology.