The DOI matches its Crossref record.
A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
Open accessAbstract
* research for this paper was supported by the United States Air Force under Contract No. AF18(600-685) monitored by the Office of Scientific Research. 1 A discussion of the problem along with the necessary references will be found in Harry Pollard, The Harmonic Analysis of Bounded Functions, Duke Math. / . , 20, 499-512, 1953. 2 See ibid. 3 See S. Bochner, Fouriersche Integrate (Leipzig, 1932), p. 33. 4 Levitan polynomial. See N.I. Achieser, Approximationstheorie (Berlin, 1953), p. 146.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Probability: Theory and Examples.
Prewitt, K., & Durrett, R. (1992) · Journal of the American Statistical Association · doi:10.2307/2290301 · Cited by 3,085
Halliday, D. M., Rosenberg, J. R., Amjad, A. M., Breeze, P., Conway, B. A., & Farmer, S. F. (1995) · Progress in Biophysics and Molecular Biology · doi:10.1016/s0079-6107(96)00009-0 · Cited by 1,107
Fairness in Criminal Justice Risk Assessments: The State of the Art
Berk, R., Heidari, H., Jabbari, S., Kearns, M., & Roth, A. (2021) · Sociological Methods & Research · doi:10.1177/0049124118782533 · Cited by 988
“The IID requirement can be relaxed somewhat (Rosenblatt 1956; Wu 2005).”
BackgroundProbability: Theory and Examples
Durrett, R. (2019) · doi:10.1017/9781108591034 · Cited by 857
Nonlinear system theory: Another look at dependence
Wu, W. B. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0506715102 · Cited by 572
Metadata
- Authors
- Rosenblatt, M.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 1956-01
- Volume
- 42
- Issue
- 1
- Pages
- 43-47
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2056871913
- Cited by
- 1,365
- References
- 0
- FWCI
- 1.79
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION. https://app.cochat.ai/papers/10.1073/pnas.42.1.43
- The paper
- Rosenblatt, M. (1956). A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.42.1.43
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
