Mathlib Map

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
Defined in
Mathlib.Analysis.InnerProductSpace.Continuous
Cited by
15 results in Mathlib
Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeSeminormedAddCommGroupInnerProductSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.ext_of_charFun · cited by 7Measure.ext_of_charFunMeasureTheory.AEStronglyMeasurable.inner · cited by 6AEStronglyMeasurable.innerBoundedContinuousFunction.innerProbChar · cited by 5BoundedContinuousFunction…Filter.Tendsto.inner · cited by 3Tendsto.innerMeasurable.inner · cited by 3Measurable.innerSchwartzMap.integral_bilin_fourier_eq · cited by 3SchwartzMap.integral_bili…Orientation.continuousAt_oangle · cited by 2Orientation.continuousAt_…MeasureTheory.Measure.ext_of_complexMGF_eq · cited by 1Measure.ext_of_complexMGF…SchwartzMap.integral_sesq_fourier_eq · cited by 1SchwartzMap.integral_sesq…UniformSpace.Completion.inner_coe · cited by 1Completion.inner_coeMeasureTheory.ProbabilityMeasure.tendsto_charPoly_of_tendsto_charFun · cited by 1ProbabilityMeasure.tendst…MeasureTheory.ProbabilityMeasure.tendsto_of_tendsto_charFun · cited by 1ProbabilityMeasure.tendst…Real.tendsto_integral_gaussian_smul · cited by 1Real.tendsto_integral_gau…UniformSpace.Completion.continuous_inner · cited by 1Completion.continuous_inn…Inseparable.inner_eq_inner · cited by 0Inseparable.inner_eq_innerInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupContinuous · cited by 2592ContinuousInner.inner · cited by 1089Inner.innerIsBoundedBilinearMap.continuous · cited by 11IsBoundedBilinearMap.cont…isBoundedBilinearMap_inner · cited by 6isBoundedBilinearMap_innercontinuous_innerCITED BYCITES

Cites7

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

Cited by16

Results whose statement or proof uses this declaration.