Alphabeta MathHow 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.
Two results called Mazur's lemma
Remark
Under the Axiom of Choice (The Axiom of Choice), this page proves the result usually called Mazur's theorem: norm and weak closures of a convex set coincide (Mazur theorem: weak and norm closure agree for convex sets). Another result often called Mazur's lemma says that suitable convex combinations of a weakly convergent sequence converge in norm. That sequence-level result is not proved or used here.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 results within two dependency steps 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
- Gerald Teschl, Topics in Real and Functional Analysis, Theorem 5.11 (standard reference, not scraped)