Theorems · Theorem · measure theory
MeasureTheory.Measure.LebesgueDecomposition.iSup_succ_eq_sup
∀ {α : Sort u_2} (f : ℕ → α → ENNReal) (m : ℕ) (a : α),
⨆ k, ⨆ (_ : k ≤ m + 1), f k a = max (f m.succ a) (⨆ k, ⨆ (_ : k ≤ m), f k a)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- LE.le.transproof · cited by 3,151
- iSupstatement and proof · cited by 2,415
- le_rflproof · cited by 1,558
- le_sup_leftproof · cited by 265
- sup_leproof · cited by 159
- iSup₂_leproof · cited by 96
- le_antisymm_iffproof · cited by 62
- le_iSup₂proof · cited by 56
- le_sup_of_le_rightproof · cited by 17
- biSup_monoproof · cited by 15
- Nat.of_le_succproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLEproof · cited by 2