Theorems · Theorem · real analysis

LipschitzWith.comp_locallyBoundedVariationOn

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {F : Type u_3}
  [inst_2 : PseudoEMetricSpace F] {f : E → F} {C : NNReal},
  LipschitzWith C f → ∀ {g : α → E} {s : Set α}, LocallyBoundedVariationOn g s → LocallyBoundedVariationOn (f ∘ g) s

Defined in: Mathlib.Topology.EMetricSpace.BoundedVariation
Cited by: 2 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder PseudoEMetricSpace PseudoEMetricSpace

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
LinearOrderstatement and proof · cited by 8,572
NNRealstatement and proof · cited by 4,310
PseudoEMetricSpacestatement and proof · cited by 1,536
LipschitzWithstatement and proof · cited by 316
Set.mapsTo_univproof · cited by 55
LocallyBoundedVariationOnstatement and proof · cited by 41
LipschitzWith.lipschitzOnWithproof · cited by 16
LipschitzOnWith.comp_locallyBoundedVariationOnproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

LocallyBoundedVariationOn.ae_differentiableWithinAt_of_memproof · cited by 4
LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_piproof · cited by 1