Theorems · Theorem · probability
Finset.expect_const
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Module ℚ≥0 M] {s : Finset ι},
s.Nonempty → ∀ (a : M), (s.expect fun _i => a) = a- Defined in
- Mathlib.Algebra.BigOperators.Expect
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.cardproof · cited by 2,327
- Nat.cast_zeroproof · cited by 1,870
- Finset.Nonemptystatement and proof · cited by 1,001
- NNRatstatement and proof · cited by 523
- Finset.sum_constproof · cited by 254
- Finset.expectstatement · cited by 116
- Nat.cast_smul_eq_nsmulproof · cited by 110
- inv_smul_smul₀proof · cited by 80
- Finset.Nonempty.card_ne_zeroproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Fintype.expect_constproof · cited by 1
- AddChar.wInner_cWeight_selfproof · cited by 1
- Finset.expect_ltproof · cited by 0
- Finset.exists_le_of_expect_leproof · cited by 0
- Finset.exists_le_of_le_expectproof · cited by 0
- AddDissociated.randomisationproof · cited by 0
- Fintype.balance_idemproof · cited by 0
- Finset.lt_expectproof · cited by 0