Theorems · Theorem · functional analysis
continuous_inner
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E],
Continuous fun p => inner 𝕜 p.1 p.2- Cited by
- 15 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Continuousstatement · cited by 2,592
- Inner.innerstatement · cited by 1,089
- IsBoundedBilinearMap.continuousproof · cited by 11
- isBoundedBilinearMap_innerproof · cited by 6
Cited by16
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.ext_of_charFunproof · cited by 7
- MeasureTheory.AEStronglyMeasurable.innerproof · cited by 6
- BoundedContinuousFunction.innerProbCharproof · cited by 5
- Filter.Tendsto.innerproof · cited by 3
- Measurable.innerproof · cited by 3
- SchwartzMap.integral_bilin_fourier_eqproof · cited by 3
- Orientation.continuousAt_oangleproof · cited by 2
- MeasureTheory.Measure.ext_of_complexMGF_eqproof · cited by 1
- SchwartzMap.integral_sesq_fourier_eqproof · cited by 1
- UniformSpace.Completion.inner_coeproof · cited by 1
- MeasureTheory.ProbabilityMeasure.tendsto_charPoly_of_tendsto_charFunstatement and proof · cited by 1
- MeasureTheory.ProbabilityMeasure.tendsto_of_tendsto_charFunproof · cited by 1