Le théorème de lebesgue sur la dérivabilité des fonctions à variation bornée
Bibliographic record
Abstract
Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants\net des plus importants de l'analyse mathématique ; à savoir qu'une fonction\nà variation bornée est dérivable presque partout. Le but de ce travail est de fournir,\nà part la démonstration souvent proposée dans les cours de la théorie de la\nmesure, d'autres démonstrations élaborées avec des outils mathématiques plus\nsimples. Ma contribution a consisté essentiellement à détailler et à compléter ces\ndémonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité.\nNous allons maintenant, pour ce théorème qui se présente sous d'autres variantes,\nen proposer l'historique et trois démonstrations différentes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.018 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".