Prevalence Theory: A Measure-theoretic Approach to Large Sets in Infinite-Dimensional Spaces

The concept of prevalence provides a rigorous framework for identifying ``large'' sets in infinite-dimensional spaces, extending measure-theoretic ideas of negligibility beyond finite-dimensional contexts. This paper introduces the foundational definitions of prevalence, exploring its key properties and illustrating its relevance through examples in functional spaces. We also investigate the interplay between prevalent sets and Baire categories, emphasizing that while these notions share certain structural parallels, they are fundamentally distinct.