Theorems · Definition · harmonic analysis
Fintype.balance
{ι : Type u_1} → {G : Type u_4} → [Fintype ι] → [inst : AddCommGroup G] → [Module ℚ≥0 G] → (ι → G) → ι → GThe balancing of a function, namely the function minus its average.
- Defined in
- Mathlib.Algebra.BigOperators.Balance
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeAddCommGroupModule
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
- AddCommGroupstatement and proof · cited by 12,871
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- NNRatstatement and proof · cited by 523
- Finset.expectproof · cited by 116
Cited by17
Results whose statement or proof uses this declaration.
- Complex.re_balancestatement · cited by 1
- Fintype.sum_balancestatement · cited by 1
- Fintype.map_balancestatement · cited by 1
- Complex.im_balancestatement · cited by 1
- Complex.ofReal_balancestatement · cited by 1
- RCLike.ofReal_balancestatement · cited by 1
- Complex.re_comp_balancestatement · cited by 0
- Fintype.expect_balancestatement and proof · cited by 0
- Complex.im_comp_balancestatement · cited by 0
- Fintype.balance_addstatement · cited by 0
- Fintype.balance_applystatement · cited by 0
- Fintype.balance_idemstatement · cited by 0