Theorems · Theorem · probability
Finset.expect_mul
∀ {ι : Type u_1} {M : Type u_4} [inst : Semiring M] [inst_1 : Module ℚ≥0 M] [IsScalarTower ℚ≥0 M M] (s : Finset ι)
(f : ι → M) (a : M), (s.expect fun i => f i) * a = s.expect fun i => f i * a- Defined in
- Mathlib.Algebra.BigOperators.Expect
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringModuleIsScalarTower
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- Finset.sumproof · cited by 5,195
- IsScalarTowerstatement and proof · cited by 3,896
- Finset.cardproof · cited by 2,327
- NNRatstatement and proof · cited by 523
- Finset.expectstatement and proof · cited by 116
- Finset.sum_mulproof · cited by 112
- smul_mul_assocproof · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- Finset.expect_mul_expectproof · cited by 1
- AddDissociated.randomisationproof · cited by 0
- Finset.expect_divproof · cited by 0