Theorems · Definition · probability
Finset.expect
{ι : Type u_1} → {M : Type u_4} → [inst : AddCommMonoid M] → [Module ℚ≥0 M] → Finset ι → (ι → M) → MAverage of a function over a finset. If the finset is empty, this is equal to zero.
- Defined in
- Mathlib.Algebra.BigOperators.Expect
- Cited by
- 116 results in Mathlib
- Foundations
- Depth 90 from the axioms, rests on 1,341 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumproof · cited by 5,195
- Finset.cardproof · cited by 2,327
- NNRatstatement and proof · cited by 523
Cited by117
Results whose statement or proof uses this declaration.
- Finset.expect_congrstatement and proof · cited by 19
- Fintype.balanceproof · cited by 17
- Finset.expect_conststatement · cited by 8
- map_expectstatement · cited by 7
- Finset.expect_emptystatement · cited by 5
- Finset.expect_lt_expectstatement · cited by 4
- RCLike.wInner_cWeight_eq_expectstatement · cited by 4
- Finset.expect_mulstatement and proof · cited by 3
- AddChar.expect_eq_zero_iff_ne_zerostatement · cited by 3
- Finset.mul_expectstatement and proof · cited by 3
- Finset.card_smul_expectstatement · cited by 3
- Finset.expect_const_zerostatement · cited by 3