Borelmessbare
Borelmessbare is the German term for Borel-measurable, used to describe functions or sets that are measurable with respect to the Borel sigma-algebra on a topological space. In mathematics, this concept plays a central role in measure theory and probability theory.
Definition: Let X be a topological space with its Borel sigma-algebra B(X), generated by the open sets,
Examples and properties: Every continuous function between topological spaces is Borelmessbar, since the preimage of any
Relation to other measurability concepts: The Borel sigma-algebra is the smallest sigma-algebra containing all open sets.
Uses: Borelmessbare functions are foundational in integration, probability, and functional analysis, enabling the definition of random