Finitely Additive Measures on Topological Spaces and Boolean Algebras, University of East Anglia, UK, 2015. Supervised by Mirna Džamonja
Bibliographic record
Abstract
The thesis studies some problems in measure theory.In particular, a possible generalization corresponding to Maharam Theorem for finitely additive measures (charges).In Chapter one, we give some definitions and results on different areas of Mathematics that will be used during this work.In Chapter two, we recall the definitions of nonatomic, continuous and Darboux charges, and show their relations to each other.The relation between charges on Boolean algebras and the induced measures on their Stone spaces is mentioned in this chapter.We also show that for any charge algebra, there exists a compact zero-dimensional space such that its charge algebra is isomorphic to the given charge algebra.In Chapter three, we give the definition of Jordan measure and some of its outcomes.We define another measure on an algebra of subsets of some sets called Jordanian measure, and investigate it.Then we define the Jordan algebras and Jordanian algebras and study some of their properties.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.050 | 0.010 |
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".