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.
Positive linear functionals on
Definition
A real-linear map is positive if pointwise implies . This is a real notion; no global uniform-norm bound is part of the definition. The bounded complex result is stated separately below.
Depends on
Used by
- Left Haar integral and left Haar measure Definition
- Every positive linear functional on C_c(X) is uniformly sup-norm bounded False statement
- A positive linear functional on C_c(X) is monotone Lemma
- The RMK functional outer content is well defined Lemma
- The distributional Riesz functional of a subharmonic function is a positive Radon measure Theorem
Dependency tree · two levels
4 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
- Donald L. Cohn, Measure Theory, 2nd ed., §7.2 (standard reference, not scraped)