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Riesz: representation of linear functional operations

Contribution grade

Analysis · THEOREM

Reference score300,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Represented continuous linear functionals on C[0,1] as Stieltjes integrals against bounded-variation functions.

Scientific scope

The record is Riesz's sole-author 1909 Comptes rendus note and its C[a,b] representation result. Because the original note was not directly inspected, the claim is limited to Riesz's later proofs and retrospective account; it does not absorb the distinct Hilbert-space representation theorem, later measure representations or all of functional analysis.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is Riesz's sole-author 1909 Comptes rendus note and its C[a,b] representation result. Because the original note was not directly inspected, the claim is limited to Riesz's later proofs and retrospective account; it does not absorb the distinct Hilbert-space representation theorem, later measure representations or all of functional analysis.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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