Theorems · Theorem · functional analysis
HasCompactMulSupport.exists_pos_le_norm
∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddGroup α] {f : α → E} [inst_1 : One E],
HasCompactMulSupport f → ∃ R, 0 < R ∧ ∀ (x : α), R ≤ ‖x‖ → f x = 1- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddGroupOne
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Cites13
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
- add_pos'proof · cited by 88
- HasCompactMulSupportstatement and proof · cited by 43
- NormedAddGroupstatement and proof · cited by 32
- IsCompact.isBoundedproof · cited by 29
- lt_add_of_le_of_posproof · cited by 11
- Bornology.IsBounded.exists_pos_norm_leproof · cited by 4
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