Theorems · Theorem · functional analysis
Seminorm.finset_sup_apply
∀ {𝕜 : Type u_3} {E : Type u_7} {ι : Type u_11} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E]
[inst_2 : Module 𝕜 E] (p : ι → Seminorm 𝕜 E) (s : Finset ι) (x : E),
(s.sup p) x = ↑(s.sup fun i => NNReal.mk ((p i) x) ⋯)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Bot.botproof · cited by 4,720
- NNRealstatement and proof · cited by 4,310
- Nat.cast_zeroproof · cited by 1,870
- NNReal.toRealstatement and proof · cited by 1,260
- Finset.supstatement and proof · cited by 530
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
Cited by7
Results whose statement or proof uses this declaration.
- Seminorm.ball_finset_sup_eq_iInterproof · cited by 5
- Seminorm.finset_sup_apply_ltproof · cited by 2
- Seminorm.exists_apply_eq_finset_supproof · cited by 2
- Seminorm.closedBall_finset_sup_eq_iInterproof · cited by 1
- Seminorm.finset_sup_smulproof · cited by 1
- SeminormFamily.finset_sup_compproof · cited by 1
- Seminorm.finset_sup_apply_leproof · cited by 0