Theorems · Theorem · functional analysis
gauge_le_one_of_mem
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {x : E}, x ∈ s → gauge s x ≤ 1- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- one_smulproof · cited by 1,374
- zero_le_oneproof · cited by 316
- gaugestatement · cited by 85
- gauge_le_of_memproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- self_subset_setOfPred_gauge_le_oneproof · cited by 2
- gauge_le_one_iff_mem_closureproof · cited by 2