Theorems · Theorem · measure theory
MeasureTheory.lmarginal_empty
∀ {δ : Type u_1} {X : δ → Type u_3} [inst : (i : δ) → MeasurableSpace (X i)] (μ : (i : δ) → MeasureTheory.Measure (X i))
[inst_1 : DecidableEq δ] (f : ((i : δ) → X i) → ENNReal), ∫⋯∫⁻_∅, f ∂μ = f- Defined in
- Mathlib.MeasureTheory.Integral.Marginal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpaceDecidableEq
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.
- Finsetstatement · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.lintegralproof · cited by 1,152
- isEmptyElimproof · cited by 59
- Function.updateFinsetproof · cited by 46
- MeasureTheory.lmarginalstatement · cited by 28
- MeasureTheory.lintegral_dirac'proof · cited by 19
- MeasureTheory.Measure.pi_of_emptyproof · cited by 6
- Subsingleton.measurableproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.GridLines.T_emptyproof · cited by 1
- MeasureTheory.lintegral_mul_prod_lintegral_pow_leproof · cited by 1
- MeasureTheory.lmarginal_imageproof · cited by 0
- MeasureTheory.lmarginal_update_of_notMemproof · cited by 0