Theorems · Theorem · general topology
HolderWith.edist_le_of_le
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal}
{f : X → Y}, HolderWith C r f → ∀ {x y : X} {d : ENNReal}, edist x y ≤ d → edist (f x) (f y) ≤ ↑C * d ^ ↑r- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- Set.univproof · cited by 3,945
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement · cited by 1,260
- EDist.ediststatement and proof · cited by 735
- HolderWithstatement and proof · cited by 47
- HolderWith.holderOnWithproof · cited by 8
- HolderOnWith.edist_le_of_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- HolderWith.ediam_image_leproof · cited by 0