On a group analogue of the Heyde theorem

Margaryta Myronyuk

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On a group analogue of the Heyde theorem

Margaryta Myronyuk

Probability · Submitted 14 Jun 2019

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

The authors' main claim The present article is devoted to an analog of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.

how it is stated · asserted 0.87 read the record →

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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, 2,274 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.17 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.03 · compares with prior results 0.70 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analog of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another.	background 1.00	0.02	0.05	asserted 1.00
s1	The present article is devoted to an analog of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.	contribution 0.99	0.44	0.11	asserted 0.87

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v2

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

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analog of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.

Human review

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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