Theorems · Theorem · general topology
MemHolder.nnHolderNorm_add_le
∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : NormedAddCommGroup Y] {r : NNReal} {f g : X → Y},
MemHolder r f → MemHolder r g → nnHolderNorm r (f + g) ≤ nnHolderNorm r f + nnHolderNorm r g- Defined in
- Mathlib.Topology.MetricSpace.HolderNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- MetricSpacestatement and proof · cited by 1,684
- MemHolderstatement and proof · cited by 26
- nnHolderNormstatement · cited by 13
- MemHolder.holderWithproof · cited by 7
- MemHolder.addproof · cited by 2
- HolderWith.addproof · cited by 2
- HolderWith.nnholderNorm_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- eHolderNorm_add_leproof · cited by 0