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Bands in $L_p$-spaces

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Hendrik Vogt, Jürgen Voigt

Functional Analysis · Submitted 24 Mar 2016

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

The authors' main claim For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$.

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arXiv ID1603.07681 (version 3)
Pith ID4V6MPOG5, Pith's permanent record of this paper and its review
CitationHendrik Vogt, J\"urgen Voigt. "Bands in $L_p$-spaces." arXiv:1603.07681 (2016). https://pith.science/paper/4V6MPOG5
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,384 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$. The theory is illustrated by an example, with an application to absorption semigroups.

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 For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$. result 0.96 0.90 0.93 asserted 1.00
s1 The theory is illustrated by an example, with an application to absorption semigroups. contribution 0.63 0.83 0.03 asserted 0.98

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

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  • arXiv listing abstract v3
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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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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

For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu^{\prime\prime}$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu^{\prime\prime}\text{-a.e.}\}$. The theory is illustrated by an example, with an application to absorption semigroups.

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