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Examples of Groups that are Measure Equivalent to the Free Group

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Damien Gaboriau (UMPA-ENSL)

Dynamical Systems · Submitted 9 Mar 2005

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

The authors' main claim We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group.

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arXiv IDmath/0503181 (version 2)
Pith IDOQ5NZRA7, Pith's permanent record of this paper and its review
CitationDamien Gaboriau (UMPA-ENSL). "Examples of Groups that are Measure Equivalent to the Free Group." arXiv:math/0503181 (2005). https://pith.science/paper/OQ5NZRA7
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,142 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.35 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.

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 Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. background 1.00 0.04 0.02 asserted 1.00
s1 This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. background 1.00 0.05 0.02 asserted 1.00
s2 On the other hand, contructions of ME equivalent groups are very rare. gap 0.87 0.05 0.02 asserted 1.00
s3 We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. contribution 1.00 0.97 0.90 asserted 1.00
s4 We also present a quite extensive survey on results about Measure Equivalence for countable groups. contribution 0.98 0.75 0.03 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.93 · evidence from proof or derivation 0.98.

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  • references and citing sentences
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  • P abstract
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  • 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

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.

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