Riemann: a definition and criterion for definite integrability

What changed

Integration acquired a workable condition for bounded functions with discontinuities.

Scientific scope

1854 habilitation manuscript and its later publication; no claim to Darboux or Lebesgue's subsequent theories.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is bounded to the integration treatment in Riemann’s 1854 habilitation work. Later Riemann-integration textbooks, Darboux formulations and Lebesgue integration are separate.

Contributors

• Bernhard Riemann · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Kalliope record for Riemann’s 1854 habilitation manuscript
• Riemann, On the representation of a function by a trigonometric series

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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