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A proof of Sanov's Theorem via discretizations

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Rangel Baldasso, Roberto I. Oliveira, Alan Pereira, Guilherme Reis

Probability · Submitted 8 Dec 2021

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

The authors' main claim We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments.

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arXiv ID2112.04280 (version 2)
Pith IDBRVKLNUR, Pith's permanent record of this paper and its review
CitationAlan Pereira, Guilherme Reis, Rangel Baldasso, Roberto I. Oliveira. "A proof of Sanov's Theorem via discretizations." arXiv:2112.04280 (2021). https://pith.science/paper/BRVKLNUR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,887 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite discretizations of the Polish space. The main tool in our proof is an explicit control on the rate of convergence for the approximated measures.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. contribution 1.00 0.94 0.75 asserted 1.00
s1 We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite discretizations of the Polish space. method 0.98 0.82 0.11 asserted 0.99
s2 The main tool in our proof is an explicit control on the rate of convergence for the approximated measures. method 0.87 0.87 0.15 asserted 1.00

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

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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 present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite discretizations of the Polish space. The main tool in our proof is an explicit control on the rate of convergence for the approximated measures.

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