DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

The lambda-system generated by a family of sets

Definition

Let $X$ be a set and $E \subseteq P (X)$ . The lambda-system generated by $E$ is

$λ_{X} (E) : = ⋂ {D : D is a lambda-system on X and E \subseteq D} .$

Write $λ (E)$ when $X$ is clear. That the intersection is taken over a nonempty family and is itself a lambda-system is proved in The generated lambda-system exists and is minimal ↗.

Depends on

Lambda-systems, or Dynkin systems

Used by

The generated lambda-system exists and is minimal Lemma

Dependency tree · one level

1 result within one dependency step of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

A. Dembo, Probability Theory lecture notes, proof of Theorem 1.1.38 (standard reference, not scraped)