Branches of Mathematics
Measure Theory
Also Known As Lebesgue Measure Theory
Citation Formats
General Reference
APA Style
BibTeX
Measure theory generalises the intuitive notions of length, area and volume into a rigorous framework for assigning a size to a set, providing the foundation on which modern integration and probability are built. Its modern form was laid out by Emile Borel, Henri Lebesgue, Constantin Caratheodory and others in the late nineteenth and early twentieth centuries.
Facts
Central QuestionWhich subsets of a space can be assigned a consistent, countably additive notion of size, and how does that assignment let integration be defined rigorously over them? 1 Key DebateWhether every subset of the real line can be measured at all: Giuseppe Vitali's 1905 construction of a non-measurable set, sharpened two decades later by the Banach-Tarski paradox, showed that no measure extending ordinary length can consistently be defined on every subset without contradiction. 1 Cross-Tradition Connections
Sources
Reader Challenges (0 open reader challenges)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.
View At A Past Year
The atlas records no dated fact of its own for this entry, so there is no other year to choose.