Theorems · Theorem · real analysis
sum_div_card_sq_le_sum_sq_div_card
∀ {ι : Type u_1} {α : Type u_2} [inst : Semifield α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [ExistsAddOfLE α]
{s : Finset ι} {f : ι → α}, ((∑ i ∈ s, f i) / ↑s.card) ^ 2 ≤ (∑ i ∈ s, f i ^ 2) / ↑s.card- Defined in
- Mathlib.Algebra.Order.Chebyshev
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finset.cardstatement and proof · cited by 2,327
- mul_assocproof · cited by 1,667
- le_of_ltproof · cited by 1,175
- Finset.Nonemptyproof · cited by 1,001
- Semifieldstatement and proof · cited by 439
- zero_powproof · cited by 361
- CharP.cast_eq_zeroproof · cited by 357
- ExistsAddOfLEstatement and proof · cited by 330
Cited by3
Results whose statement or proof uses this declaration.
- SzemerediRegularity.edgeDensity_chunk_uniformproof · cited by 1
- SzemerediRegularity.add_div_le_sum_sq_div_cardproof · cited by 1
- SzemerediRegularity.mul_sq_le_sum_sqproof · cited by 1