Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
∀ {Ω : Type u_1} [inst : Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : MeasureTheory.FiniteMeasure Ω),
μ ≠ 0 → ∀ (s : Set Ω), μ.normalize s = μ.mass⁻¹ * μ s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- NNRealstatement · cited by 4,310
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.ProbabilityMeasurestatement · cited by 127
- inv_mul_cancel_left₀proof · cited by 47
- MeasureTheory.FiniteMeasure.massstatement and proof · cited by 46
- MeasureTheory.FiniteMeasure.normalizestatement and proof · cited by 15
- MeasureTheory.FiniteMeasure.mass_nonzero_iffproof · cited by 6
- MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalizeproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzeroproof · cited by 1
- ProbabilityMeasure.toFiniteMeasure_normalize_eq_selfproof · cited by 0