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Minimal elements of stopping time $\sigma$-algebras

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Tom Fischer

Probability · Submitted 12 Dec 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration.

how it is stated · asserted 1.00 read the record →

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arXiv ID1112.2537 (version 3)
Pith IDIFI2RMBH, Pith's permanent record of this paper and its review
CitationTom Fischer. "Minimal elements of stopping time $\sigma$-algebras." arXiv:1112.2537 (2011). https://pith.science/paper/IFI2RMBH
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,262 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An example is provided.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. result 0.59 0.94 0.91 asserted 1.00
s1 This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An example is provided. interpretation 0.98 0.83 0.10 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An example is provided.

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