Theorems · Theorem · real analysis
BoxIntegral.integralSum_inf_partition
∀ {ι : Type u} {E : Type v} {F : Type w} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {I : BoxIntegral.Box ι} (f : (ι → ℝ) → E)
(vol : BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤) (π : BoxIntegral.TaggedPrepartition I)
{π' : BoxIntegral.Prepartition I},
π'.IsPartition → BoxIntegral.integralSum f vol (π.infPrepartition π') = BoxIntegral.integralSum f vol π- Defined in
- Mathlib.Analysis.BoxIntegral.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- ContinuousLinearMapstatement and proof · cited by 5,352
- WithTopstatement · cited by 3,754
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.TaggedPrepartitionstatement and proof · cited by 126
- BoxIntegral.BoxAdditiveMapstatement and proof · cited by 92
- BoxIntegral.TaggedPrepartition.toPrepartitionproof · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- BoxIntegral.integralSum_sub_partitionsproof · cited by 1