Theorems · Theorem · global analysis

contMDiffWithinAt_finsetSum

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {n : WithTop ℕ∞} {H : Type u_3}
  [inst_1 : TopologicalSpace H] {E : Type u_4} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E]
  {I : ModelWithCorners 𝕜 E H} {G : Type u_5} [inst_4 : AddCommMonoid G] [inst_5 : TopologicalSpace G]
  [inst_6 : ChartedSpace H G] [ContMDiffAdd I n G] {E' : Type u_6} [inst_8 : NormedAddCommGroup E']
  [inst_9 : NormedSpace 𝕜 E'] {H' : Type u_7} [inst_10 : TopologicalSpace H'] {I' : ModelWithCorners 𝕜 E' H'}
  {M : Type u_8} [inst_11 : TopologicalSpace M] [inst_12 : ChartedSpace H' M] {s : Set M} {x : M} {t : Finset ι}
  {f : ι → M → G},
  (∀ i ∈ t, ContMDiffWithinAt I' I n (f i) s x) → ContMDiffWithinAt I' I n (fun x => ∑ i ∈ t, f i x) s x

Defined in

Mathlib.Geometry.Manifold.Algebra.Monoid

Cited by

3 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceAddCommMonoidTopologicalSpaceChartedSpaceContMDiffAddNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace