Lebesguemessbare
Lebesgue-measurable (Lebesgue-messbare) is a central concept in measure theory referring to subsets of Euclidean space and to functions that are compatible with Lebesgue measure. It provides a framework for integration that extends beyond Riemann theory and handles a wider class of sets and functions.
For sets, a subset E of R^n is Lebesgue measurable if it satisfies Carathéodory’s criterion: for every
For functions, a function f: R^n → R (or extended real) is Lebesgue measurable if the preimage of
Lebesgue measure and measurability enable powerful convergence and integration theorems, such as the dominated convergence theorem,