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@article{huhn2009,
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@inproceedings{smithGal2018,
  author       = {Lewis Smith and
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  optEditor       = {Amir Globerson and
                  Ricardo Silva},
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  booktitle    = {Proc.\ UAI, 34th Conference on Uncertainty in Artificial
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  optPublisher    = {{AUAI} Press},
  year         = {2018}
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@article{Hinton06,
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@book{goodfellow2016deep,
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@book{popper2014conjectures,
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@InProceedings{caprio-gong,
	title = 	 {Dynamic precise and imprecise probability kinematics},
	author =       {Caprio, Michele and Gong, Ruobin},
	booktitle = 	 {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications},
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	year = 	 {2023},
	volume = 	 {215},
	series = 	 {Proceedings of Machine Learning Research},
	publisher =    {PMLR}
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@article{caprio_IBNN,
	title={{Imprecise Bayesian neural networks}},
	author={Michele Caprio and Souradeep Dutta and Radoslav Ivanov and Kuk Jang and Vivian Lin and Oleg Sokolsky and Insup Lee},
	journal={arXiv preprint arXiv:2302.09656},
	year={2023}
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@inproceedings{smets,
  title={About Updating},
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@Inproceedings{Bottou2013,
	author={Bottou, L{\'e}on},
	editor={Sch{\"o}lkopf, Bernhard
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	and Vovk, Vladimir},
	title={In Hindsight: Doklady Akademii Nauk {SSSR}, 181(4), 1968},
	bookTitle={Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik},
	year={2013},
	publisher={Springer},
	optaddress={Berlin, Heidelberg},
	pages={3--5},
	abstract={This short contribution presents the first paper in which Vapnik and Chervonenkis describe the foundations of Statistical Learning Theory (Vapnik, Chervonenkis (1968) Proc USSR Acad Sci 181(4): 781--783).},
	optisbn={978-3-642-41136-6},
	optdoi={10.1007/978-3-642-41136-6_1},
	opturl={https://doi.org/10.1007/978-3-642-41136-6_1}
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@inproceedings{mosler,
	author={Mosler, Karl},
	title={Zonoids and lift zonoids},
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	year={2002},
	publisher={New York : Springer},
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@article{shelah1972combinatorial,
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@inproceedings{bronevich2008axioms,
	title={{Axioms for Uncertainty Measures on Belief Functions and Credal Sets}},
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	pages={1--6},
	year={2008},
	organization={IEEE}
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@article{pal1993uncertainty,
	title={{Uncertainty Measures for Evidential Reasoning {II}: {A} New Measure of Total Uncertainty}},
	author={Pal, Nikhil R and Bezdek, James C and Hemasinha, Rohan},
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@inproceedings{duan2023evidential,
  author       = {Ruxiao Duan and
                  Brian Caffo and
                  Harrison X. Bai and
                  Haris I. Sair and
                  Craig Jones},
  title        = {Evidential Uncertainty Quantification: {A} Variance-Based Perspective},
  booktitle    = {{IEEE/CVF} Winter Conference on Applications of Computer Vision, {WACV}
                  2024, Waikoloa, HI, USA, January 3-8, 2024},
  pages        = {2121--2130},
  publisher    = {{IEEE}},
  year         = {2024},
  timestamp    = {Wed, 17 Apr 2024 11:21:26 +0200},
  biburl       = {https://dblp.org/rec/conf/wacv/DuanCBSJ24.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
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@article{xiaoFashion2017,
  author       = {Han Xiao and
                  Kashif Rasul and
                  Roland Vollgraf},
  title        = {Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning
                  Algorithms},
  journal      = {CoRR},
  volume       = {abs/1708.07747},
  year         = {2017},
  eprinttype    = {arXiv},
  eprint       = {1708.07747},
  timestamp    = {Mon, 13 Aug 2018 16:47:27 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1708-07747.bib},
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@article{Sauer1972density,
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	year = "1972",
	optIssn = "0097-3165",
	optDoi = "https://doi.org/10.1016/0097-3165(72)90019-2",
	url = "http://www.sciencedirect.com/science/article/pii/0097316572900192",
	author = "N Sauer",
	abstract = "If T is a family of sets and A some set we denote by T ∩ A the following family of subsets of A: T ∩ A = {F ∩ A; FϵT}. P. Erdös (oral communication) transmitted to me in Nice the following question: Is it true that if T is a family of subsets of some infinite set S then either there exists to each number n a set A ⊂ S with |A| = n such that |T ∩ A| = 2n or there exists some number N such that |T ∩ A| ⩽ |A|c for each A ⊂ S with |A| ⩾ N and some constant c? In this paper we will answer this question in the affirmative by determining the exact upper bound. (Theorem 2).1"
}
@book{pajor1985sous,
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@book{Vapnik2006b,
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@article{serfling1974probability,
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@book{vapnik2013nature,
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@book{vapnik2006estimation,
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	author={Vapnik, Vladimir},
	year={2006},
	publisher={Springer}
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@inproceedings{vapnik1968uniform,
	title={The uniform convergence of frequencies of the appearance of events to their probabilities},
	author={Vapnik, Vladimir N and Chervonenkis, Aleksei Yakovlevich},
	booktitle={Doklady Akademii Nauk},
	volume={181},
	number={4},
	pages={781--783},
	year={1968},
	organization={Russian Academy of Sciences}
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@article{vapnik1971uniform,
	title={Theory of uniform convergence of frequencies of events to their probabilities and problems of search for an optimal solution from empirical data(Average risk minimization based on empirical data, showing relationship of problem to uniform convergence of averages toward expectation value)},
	author={Vapnik, Vladimir N and Chervonenkis, Aleksei Yakovlevich},
	journal={Automation and Remote Control},
	volume={32},
	pages={207--217},
	year={1971}
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@article{bahadur1956nonexistence,
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@book{elstrodt1996mass,
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@misc{hilbert1900mathematische,
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	author={Hilbert, David},
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@book{georgii2015stochastik,
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	year={2015},
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@book{kolmogorov1933grundbegriffe,
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	year={1933}
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@book{hilbertgrundlagen,
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	year={1956}
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@article{Choquet54,
	author = {Choquet, Gustave},
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	volume = {5},
	year = {1954},
	pages = {131-295},
	doi = {10.5802/aif.53},
	zbl = {0064.35101},
	mrnumber = {18,295g},
	language = {en},
	url = {http://www.numdam.org/item/AIF_1954__5__131_0}
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@Article{Dudley1991,
	author="Dudley, R. M.
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	and Zinn, J.",
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	journal="Journal of Theoretical Probability",
	year="1991",
	month="Jul",
	day="01",
	volume="4",
	number="3",
	pages="485--510",
	abstract="A class{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}of measurable functions on a probability space is called a Glivenko-Cantelli class if the empirical measuresPnconverge to the trueP uniformly over{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}almost surely.{\$}{\$}{\backslash}widetilde{\{}F{\}}{\$}{\$}is a universal Glivenko-Cantelli class if it is a Glivenko-Cantelli Cantelli class for all lawsP on a measurable space, and a uniform Glivenko-Cantelli class if the convergence is also uniform inP. We give general sufficient conditions for the Glivenko-Cantelli and universal Glivenko-Cantelli properties and examples to show that some stronger conditions are not necessary. The uniform Glivenko-Cantelli property is characterized, under measurability assumptions, by an entropy condition.",
	issn="1572-9230",
	doi="10.1007/BF01210321",
	url="https://doi.org/10.1007/BF01210321"
}




@book{denneberg2013,
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@article{lebesgue1972oeuvres,
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@book{kreyszig1978introductory,
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@article{abellan_additivity_2005,
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@article{radev2021amortized,
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@article{cella2022validity,
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@book{weichselberger2013elementare,
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@article{shafer2008tutorial,
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@book{balasubramanian2014conformal,
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@article{senge_2014_ReliableClassificationLearning,
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@article{lambrou2010reliable,
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@article{yang2009using,
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@inproceedings{varshney2016engineering,
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@article{varshney2017safety,
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@inproceedings{kendall2017uncertainties,
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@inproceedings{depeweg2018decomposition,
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@inproceedings{kapoor2022uncertainty,
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@article{HOFFER2023109279,
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@article{Datasetgatidis2022whole,
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