DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge 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 monotone class generated by a family of sets

Definition

Let $X$ be a set and $E \subseteq P (X)$ . The monotone class generated by $E$ is

$m_{X} (E) : = ⋂ {M : M is a monotone class on X and E \subseteq M} .$

Write $m (E)$ when $X$ is clear. Its existence as a monotone class and its minimality are proved in The generated monotone class exists and is minimal ↗.

Depends on

Monotone classes of sets

Used by

The generated monotone class exists and is minimal Lemma

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 1 result over 1 level. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources

R. F. Bass, Real Analysis for Graduate Students, version 5.0, Definition 2.9 and Theorem 2.10 (standard reference, not scraped)