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 different Riesz representation theorems
Remark
For a locally compact Hausdorff space , The bounded complex dual of C_0(X) is regular complex measures identifies the complex continuous dual of with finite regular complex Borel measures, with functional norm equal to total variation. This is the Riesz–Markov–Kakutani representation. The Hilbert-space Riesz theorem is a different representation by inner-product vectors and belongs to the later Hilbert-space development. The evaluation pairing from The dual space X^* of a normed space and its dual norm is not itself an inner-product identification. No Hilbert representation theorem is used here.
Depends on
Used by
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Dependency tree · two levels
11 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
- Bühler–Salamon, Functional Analysis, Examples 1.32 and 1.37, pp.32,37 (standard reference, not scraped)