How robustly can you predict the future?
Canadian journal of mathematics, Tome 75 (2023) no. 5, pp. 1493-1515
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Hardin and Taylor proved that any function on the reals—even a nowhere continuous one—can be correctly predicted, based solely on its past behavior, at almost every point in time. They showed that one could even arrange for the predictors to be robust with respect to simple time shifts, and asked whether they could be robust with respect to other, more complicated time distortions. This question was partially answered by Bajpai and Velleman, who provided upper and lower frontiers (in the subgroup lattice of $\mathrm{Homeo}^+(\mathbb {R})$) on how robust a predictor can possibly be. We improve both frontiers, some of which reduce ultimately to consequences of Hölder’s Theorem (that every Archimedean group is abelian).
Mots-clés :
Hölder’s Theorem, Axiom of Choice, free actions, commutators, Hat Puzzles
Cox, Sean; Elpers, Matthew. How robustly can you predict the future?. Canadian journal of mathematics, Tome 75 (2023) no. 5, pp. 1493-1515. doi: 10.4153/S0008414X22000402
@article{10_4153_S0008414X22000402,
author = {Cox, Sean and Elpers, Matthew},
title = {How robustly can you predict the future?},
journal = {Canadian journal of mathematics},
pages = {1493--1515},
year = {2023},
volume = {75},
number = {5},
doi = {10.4153/S0008414X22000402},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000402/}
}
TY - JOUR AU - Cox, Sean AU - Elpers, Matthew TI - How robustly can you predict the future? JO - Canadian journal of mathematics PY - 2023 SP - 1493 EP - 1515 VL - 75 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000402/ DO - 10.4153/S0008414X22000402 ID - 10_4153_S0008414X22000402 ER -
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