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LOCAL KEISLER MEASURES AND NIP FORMULAS

Published online by Cambridge University Press:  10 June 2019

KYLE GANNON
KYLE GANNON*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN46656, USA E-mail: [email protected]
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Abstract

We study generically stable measures in the local, NIP context. We show that in this setting, a measure is generically stable if and only if it admits a natural finite approximation.

Keywords

Primary 03C68NIPKeisler measuresgeneric stability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 1279 - 1292
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Ben Yaacov, I., Continuous and random Vapnik-Chervonenkis classes. Israel Journal of Mathematics, vol. 173 (2009), no. 1, pp. 309–333.Google Scholar
Bourgain, J., Fremlin, D. H., and Talagrand, M., Pointwise compact sets of Baire-measurable functions. American Journal of Mathematics, vol. 100 (1978), no. 4, pp. 845–886.Google Scholar
Chernikov, A. and Simon, P., Definably amenable NIP groups. Journal of the American Mathematical Society, vol. 31 (2018), no. 3, pp. 609–641.Google Scholar
Chernikov, A. and Starchenko, S., Definable regularity lemmas for NIP hypergraphs, arXiv preprint, 2016, arXiv:1607.07701.Google Scholar
Conway, J. B., A Course in Functional Analysis, Graduate Texts in Mathematics, vol. 96, Springer Science & Business Media, New York, 2013.Google Scholar
Diestel, J., Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, vol. 92, Springer Science & Business Media, New York, 2012.Google Scholar
Hrushovski, E., Peterzil, Y., and Pillay, A., Groups, measures, and the NIP. Journal of the American Mathematical Society, vol. 21 (2008), no. 2, pp. 563–596.Google Scholar
Hrushovski, E. and Pillay, A., On NIP and invariant measures, arXiv preprint, 2007, arXiv:0710.2330.Google Scholar
Hrushovski, E., Pillay, A., and Simon, P., Generically stable and smooth measures in NIP theories. Transactions of the American Mathematical Society, vol. 365 (2013), no. 5, pp. 2341–2366.Google Scholar
Ibarlucía, T., The dynamical hierarchy for Roelcke precompact Polish groups. Israel Journal of Mathematics, vol. 215 (2016), no. 2, pp. 965–1009.Google Scholar
Keisler, H. J., Measures and forking. Annals of Pure and Applied Logic, vol. 34 (1987), no. 2, pp. 119–169.Google Scholar
Khanaki, K., NIP formulas and Baire 1 definability, arXiv preprint, 2017, arXiv:1703.08731.Google Scholar
Khanaki, K. and Pillay, A., Remarks on NIP in a model, arXiv preprint, 2017, arXiv:1706.04674.Google Scholar
Semadeni, Z., Banach Spaces of Continuous Functions, vol. 1, PWN Polish Scientific Publishers, Warsaw, 1971.Google Scholar
Simon, P., A Guide to NIP Theories, Cambridge University Press, Cambridge, 2015.Google Scholar
Simon, P., Rosenthal compacta and NIP formulas, arXiv preprint, 2014, arXiv:1407.5761.Google Scholar
Vapnik, V. N. and Ya Chervonenkis, A., On the uniform convergence of relative frequencies of events to their probabilities, Measures of Complexity (Vovk, V., Papadopoulos, H., and Gammerman, A., editors), Springer, Cham, 2015, pp. 11–30.Google Scholar