DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-27

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A measurable function between measurable spaces

Let $(X, A)$ and $(Y, B)$ be measurable spaces (Measurable spaces and measurable sets). A function $f : X \to Y$ is measurable when

$f^{- 1} (B) \in A for every B \in B .$

Equivalently, the family

$C_{f} : = {B \subseteq Y : f^{- 1} (B) \in A}$

is a sigma-algebra on $Y$ containing $B$ .

Depends on