Theorems · Theorem · real analysis
eVariationOn.lowerSemicontinuous_uniformOn
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (s : Set α),
LowerSemicontinuous fun f => eVariationOn f sThe map (eVariationOn · s) is lower semicontinuous for uniform convergence on s.
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- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.singleton_subset_iffproof · cited by 206
- Filter.tendsto_idproof · cited by 180
- UniformOnFunstatement and proof · cited by 150
- eVariationOnstatement · cited by 90
- LowerSemicontinuousstatement · cited by 69
- UniformOnFun.tendsto_iff_tendstoUniformlyOnproof · cited by 5
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