Theorems · Theorem · measure theory
MeasureTheory.integral_zero_measure
∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
(f : α → G), ∫ (x : α), f x ∂0 = 0- Cited by
- 50 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 10,939
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.dominatedFinMeasAdditive_weightedSMulproof · cited by 35
- MeasureTheory.integral_eq_setToFunproof · cited by 31
- MeasureTheory.setToFun_measure_zeroproof · cited by 3
Cited by50
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_of_leproof · cited by 83
- MeasureTheory.tilted_zero_measureproof · cited by 12
- ProbabilityTheory.mgf_zero_measureproof · cited by 6
- ProbabilityTheory.deriv_cgfproof · cited by 4
- MeasureTheory.measure_smul_averageproof · cited by 4
- MeasureTheory.integral_finsetSum_measureproof · cited by 4
- MeasureTheory.integral_biUnion_finsetproof · cited by 3
- InformationTheory.klDiv_zero_leftproof · cited by 3
- MeasureTheory.average_zero_measureproof · cited by 3
- ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRatproof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioiproof · cited by 2