Theorems · Theorem · measure theory
MeasureTheory.integral_fun_snd
∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
{μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
[inst_4 : NormedSpace ℝ E] [MeasureTheory.SFinite μ] (f : β → E),
∫ (z : α × β), f z.2 ∂μ.prod ν = μ.real Set.univ • ∫ (y : β), f y ∂ν- Defined in
- Mathlib.MeasureTheory.Integral.Prod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univstatement and proof · cited by 3,945
- mul_oneproof · cited by 3,885
- MeasureTheory.integralstatement and proof · cited by 1,779
- one_smulproof · cited by 1,374
- MeasureTheory.Measure.realstatement and proof · cited by 530
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.prodstatement and proof · cited by 353
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_fun_norm_addHaarproof · cited by 1
- MeasureTheory.integral_fun_fstproof · cited by 0