Lebesguetodennäköisyyden
Lebesguetodennäköisyys, often translated as Lebesgue probability, refers to the application of Lebesgue's measure theory to probability theory. Instead of relying on the Kolmogorov axioms alone, which define probability spaces in terms of sigma-algebras and measures, Lebesgue probability emphasizes the geometric and measure-theoretic underpinnings of probability.
In this framework, a probability space is viewed as a measure space (Ω, F, P) where Ω is
The connection is particularly evident when defining probability distributions on Euclidean spaces. For instance, a continuous