# Popper Functions, Lexicographical Probability, and Non-Archimedean Probability

@article{Brickhill2016PopperFL, title={Popper Functions, Lexicographical Probability, and Non-Archimedean Probability}, author={Hazel Brickhill and Leon Horsten}, journal={arXiv: Logic}, year={2016} }

Standard probability theory has been extremely successful but there are some conceptually possible scenarios, such as fair infinite lotteries, that it does not model well. For this reason alternative probability theories have been formulated. We look at three of these: Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions. We relate Popper functions to non-Archimedean probability functions (of a specific kind) by means of a…

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