Theorems · Theorem · general topology
HolderWith.dist_le_of_le
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoMetricSpace X] [inst_1 : PseudoMetricSpace Y] {C r : NNReal} {f : X → Y},
HolderWith C r f → ∀ {x y : X} {d : ℝ}, dist x y ≤ d → dist (f x) (f y) ≤ ↑C * d ^ ↑r- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 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.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- Set.univproof · cited by 3,945
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- Set.mem_univproof · cited by 416
- HolderWithstatement and proof · cited by 47
- HolderWith.holderOnWithproof · cited by 8
- HolderOnWith.dist_le_of_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HolderWith.dist_leproof · cited by 0