Theorems · Theorem · functional analysis
HasCompactSupport.exists_pos_le_norm
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddGroup α] {f : α → E} [inst_1 : Zero E],
HasCompactSupport f → ∃ R, 0 < R ∧ ∀ (x : α), R ≤ ‖x‖ → f x = 0- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddGroupZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- IsCompactproof · cited by 1,282
- zero_lt_oneproof · cited by 598
- not_leproof · cited by 328
- HasCompactSupportstatement and proof · cited by 196
- add_pos'proof · cited by 88
- NormedAddGroupstatement and proof · cited by 32
- IsCompact.isBoundedproof · cited by 29
- lt_add_of_le_of_posproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1