Theorems · Inductive type · functional analysis
ESeminormedAddMonoid
(E : Type u_8) → [TopologicalSpace E] → Type u_8
An e-seminormed monoid is an additive monoid endowed with a continuous enorm. Note that we do not ask for the enorm to be positive definite: non-trivial elements may have enorm zero.
- Defined in
- Mathlib.Analysis.Normed.Group.Defs
- Cited by
- 133 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by149
Results whose statement or proof uses this declaration.
- enorm_zerostatement and proof · cited by 44
- MeasureTheory.Integrable.addstatement and proof · cited by 42
- MeasureTheory.integrable_indicator_iffstatement and proof · cited by 30
- MeasureTheory.MemLp.addstatement and proof · cited by 24
- MeasureTheory.integrable_zerostatement and proof · cited by 22
- MeasureTheory.Integrable.indicatorstatement and proof · cited by 15
- MeasureTheory.integrableOn_conststatement and proof · cited by 15
- MeasureTheory.eLpNorm_zerostatement and proof · cited by 14
- enorm_add_lestatement and proof · cited by 11
- MeasureTheory.Integrable.smul_measure_nnrealstatement and proof · cited by 10
- MeasureTheory.eLpNorm_add_lestatement and proof · cited by 10
- MeasureTheory.Integrable.fun_addstatement · cited by 9