Theorems · Theorem · functional analysis
continuous_nnnorm
∀ {E : Type u_4} [inst : SeminormedAddGroup E], Continuous fun a => ‖a‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- Continuousstatement · cited by 2,592
- NNNorm.nnnormstatement · cited by 952
- norm_nonnegproof · cited by 725
- SeminormedAddGroupstatement and proof · cited by 331
- Continuous.subtype_mkproof · cited by 51
- continuous_normproof · cited by 36
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyMeasurable.nnnormproof · cited by 7
- measurable_nnnormproof · cited by 5
- MeasureTheory.MemLp.isProbabilityMeasure_of_indepFunproof · cited by 5
- spectrum.exists_nnnorm_eq_spectralRadius_of_nonemptyproof · cited by 3
- Continuous.nnnormproof · cited by 3
- Filter.Tendsto.nnnormproof · cited by 3
- MeasureTheory.AEStronglyMeasurable.nnnormproof · cited by 2
- MeasureTheory.pdf.IsUniform.mul_pdf_integrableproof · cited by 0
- Inseparable.nnnorm_eq_nnnormproof · cited by 0