Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not supplied‡ not proved here
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.

‡ Recorded, not proved here. This statement is included so the library can refer to it honestly, with a citation to the literature. It is not proved anywhere in this library: the track that would prove it has not been developed here yet.

A bounded functional on L∞[0,1] need not come from L1[0,1]

Remark

There exists a bounded linear functional on L∞([0,1]) that is not of the form f⟼∫01f(x)h(x) dx for any h∈L1([0,1]).

The standard witness extends point evaluation at 0 from C([0,1]) to L∞([0,1]) by Hahn-Banach. This examples page records that classical boundary fact but does not prove it here; the page-level warning already appeared in The p=∞ case is recorded but not proved here ‡.

Used by

Nothing in the library uses this result yet.

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources