# Keisler measures in the wild

@inproceedings{Conant2021KeislerMI, title={Keisler measures in the wild}, author={Gabriel Conant and Kyle Gannon and James Hanson}, year={2021} }

We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and satisfy associativity. However, we also demonstrate failures of both properties over uncountable parameter sets. In particular, we show that the Morley product of Borel definable types need not be Borel definable (correcting an erroneous result from the…

## 5 Citations

Sequential approximations for types and Keisler measures

- Mathematics, Computer Science
- 2021

It is shown that both generically stable types and Keisler measures which are finitely satisfiable over a countable model (in NIP theories) are sequentially approximated.

ASSOCIATIVITY OF THE MORLEY PRODUCT OF INVARIANT MEASURES IN NIP THEORIES

- MathematicsThe Journal of Symbolic Logic
- 2021

A new proof of associativity for the Morley (or “nonforking”) product of invariant measures in NIP theories is given.

Generic Stability and Modes of Convergence

- Mathematics
- 2022

We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.

Definable convolution and idempotent Keisler measures II

- Mathematics
- 2022

We study convolution semigroups of invariant/finitely satisfiable Keisler measures in NIP groups. We show that the ideal (Ellis) subgroups are always trivial and describe minimal left ideals in the…

Dependent measures in independent theories

- Mathematics
- 2021

We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in NIP theories) to arbitrary theories. Among…

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ASSOCIATIVITY OF THE MORLEY PRODUCT OF INVARIANT MEASURES IN NIP THEORIES

- MathematicsThe Journal of Symbolic Logic
- 2021

A new proof of associativity for the Morley (or “nonforking”) product of invariant measures in NIP theories is given.

Definable convolution and idempotent Keisler measures

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- 2022

We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting results of Glicksberg, we show that the supports of…

Sequential approximations for types and Keisler measures

- Mathematics, Computer Science
- 2021

It is shown that both generically stable types and Keisler measures which are finitely satisfiable over a countable model (in NIP theories) are sequentially approximated.

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