File size: 594 Bytes
7f37411 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | 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
|