målebarhet
Målebarhet describes whether a set or a function is compatible with a given measure in mathematics. In a measure space (X, F, μ), a subset E ⊆ X is measurable if E ∈ F. A function f: X → ℝ is measurable if the preimage of every Borel set is in F; equivalently, for every real α, the set {x ∈ X : f(x) > α} belongs to F. These definitions extend to more general target spaces with appropriate σ-algebras.
Common examples include Borel measurability on the real line, where the σ-algebra is generated by open intervals,
Non-measurable sets exist under widely accepted foundations: with the Axiom of Choice, there are subsets of
Measurability is central to many areas of analysis and probability. It enables the definition of integrals
Outside pure mathematics, målebarhet can colloquially refer to whether a property can be measured or observed