Theorems · Theorem · real analysis

BoxIntegral.HasIntegral.congr_ae

∀ {ι : Type u} {E : Type v} [inst : Fintype ι] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
  {l : BoxIntegral.IntegrationParams} {I : BoxIntegral.Box ι} {y : E} {f g : (ι → ℝ) → E}
  {μ : MeasureTheory.Measure (ι → ℝ)} [inst_3 : MeasureTheory.IsLocallyFiniteMeasure μ],
  BoxIntegral.HasIntegral I l f μ.toBoxAdditive.toSMul y →
    f =ᵐ[μ.restrict ↑I] g → l.bRiemann = false → BoxIntegral.HasIntegral I l g μ.toBoxAdditive.toSMul y

If f has integral y on a box I with respect to a locally finite measure μ and g is a.e. equal to f on I, then g has the same integral on I.

Defined in

Mathlib.Analysis.BoxIntegral.Integrability

Cited by

1 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNormedAddCommGroupNormedSpaceMeasureTheory.IsLocallyFiniteMeasure