Theorems · Theorem · commutative algebra
tendsto_smoothingFun_of_map_one_le_one
∀ {R : Type u_1} [inst : CommRing R] (μ : RingSeminorm R),
μ 1 ≤ 1 → ∀ (x : R), Filter.Tendsto (smoothingSeminormSeq μ x) Filter.atTop (nhds (smoothingFun μ x))If μ 1 ≤ 1, then smoothingFun μ x is the limit of smoothingSeminormSeq μ x
as n tends to infinity.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- RingSeminormstatement and proof · cited by 58
- smoothingFunstatement · cited by 13
- smoothingSeminormSeqstatement · cited by 5
- tendsto_smoothingFun_of_eq_zeroproof · cited by 1
- tendsto_smoothingFun_of_ne_zeroproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- smoothingFun_apply_of_map_mul_eq_mulproof · cited by 2
- isPowMul_smoothingFunproof · cited by 1
- smoothingFun_nonnegproof · cited by 1
- smoothingFun_of_map_mul_eq_mulproof · cited by 1
- smoothingFun_one_leproof · cited by 1
- tendsto_smoothingFun_compproof · cited by 0
- smoothingFun_of_powMulproof · cited by 0