| import Mathlib | |
| import OAI.MeasureTheory.FalconerCompletion.Recursion.RecursiveLoss | |
| namespace OAI | |
| /-! Angular cutoffs and derivative estimates. -/ | |
| section | |
| section | |
| open Set MeasureTheory | |
| open scoped ComplexConjugate RealInnerProductSpace | |
| namespace GraphLiteralSupport.CurrentFalconer.TreeND | |
| lemma power_div_cap {N : ℕ} {a b M : ℝ} (hM : 0≤M) (hab : a≤b) : | |
| ((2:ℝ)^N)^a*(M/((2:ℝ)^N)^b)≤M := by | |
| apply weighted_child_cap (by positivity) hab | |
| have hp : 0<((2:ℝ)^N)^b := by positivity | |
| field_simp; exact le_rfl | |
| end GraphLiteralSupport.CurrentFalconer.TreeND | |
| end | |
| end | |
| end OAI | |