Theorems · Theorem · real analysis

BoxIntegral.IntegrationParams.MemBaseSet.exists_common_compl

∀ {ι : Type u_1} [inst : Fintype ι] {I : BoxIntegral.Box ι} {c₁ c₂ : NNReal} {l : BoxIntegral.IntegrationParams}
  {r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)} {π₁ π₂ : BoxIntegral.TaggedPrepartition I},
  l.MemBaseSet I c₁ r₁ π₁ →
    l.MemBaseSet I c₂ r₂ π₂ →
      π₁.iUnion = π₂.iUnion →
        ∃ π,
          π.iUnion = ↑I \ π₁.iUnion ∧
            (l.bDistortion = true → π.distortion ≤ c₁) ∧ (l.bDistortion = true → π.distortion ≤ c₂)

Defined in

Mathlib.Analysis.BoxIntegral.Partition.Filter

Cited by

1 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Fintype