| 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 | |