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dd14c26 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | import OAI.Probability.Localization.TerminalBudget
namespace OAI
open MeasureTheory ProbabilityTheory Set
open scoped BigOperators ENNReal
namespace RepeatedLocalization
namespace FiniteEntropy
theorem finite_expected_regularization : FiniteEntropyStatement := by
refine ⟨32,fun n hn Q P hP hac hK => ?_⟩
let := hP
have hn0 : 0 < n := by omega
refine ⟨almost_sure_termination hn P Q hac hK,measurable_terminalLog hn0 P Q,?_,
terminal_depth_integrable hn P Q hac hK,?_,?_,?_⟩
· intro h hp
exact ⟨(terminal_regular hn P Q hac hK h hp).1,(terminal_regular hn P Q hac hK h hp).2.1⟩
· exact (terminal_attempts_budget hn P Q hac hK).1
· exact (terminal_attempts_budget hn P Q hac hK).2
· exact terminal_ennreal_budget hn P Q hac hK
end FiniteEntropy
end RepeatedLocalization
end OAI
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