Theorems · Definition · functional analysis

ContinuousMultilinearMap.linearDeriv

{R : Type u} →
  {ι : Type v} →
    {M₁ : ι → Type w₁} →
      {M₂ : Type w₂} →
        [inst : Semiring R] →
          [inst_1 : (i : ι) → AddCommMonoid (M₁ i)] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : (i : ι) → Module R (M₁ i)] →
                [inst_4 : Module R M₂] →
                  [inst_5 : (i : ι) → TopologicalSpace (M₁ i)] →
                    [inst_6 : TopologicalSpace M₂] →
                      ContinuousMultilinearMap R M₁ M₂ →
                        [ContinuousAdd M₂] →
                          [DecidableEq ι] → [Fintype ι] → ((i : ι) → M₁ i) → ((i : ι) → M₁ i) →L[R] M₂

The derivative of a continuous multilinear map, as a continuous linear map from ∀ i, M₁ i to M₂; see ContinuousMultilinearMap.hasFDerivAt.

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Basic

Cited by

13 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleTopologicalSpaceTopologicalSpaceContinuousAddDecidableEqFintype