Theorems · Theorem · functional analysis
gauge_le_of_mem
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {x : E} {a : ℝ},
0 ≤ a → x ∈ a • s → gauge s x ≤ a- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 118 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.
Cites12
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
- le_reflproof · cited by 2,061
- Set.smulSetstatement · cited by 608
- LE.le.eq_or_ltproof · cited by 220
- Set.mem_singleton_iffproof · cited by 172
- gaugestatement and proof · cited by 85
- csInf_leproof · cited by 51
- gauge_zeroproof · cited by 7
- Set.zero_smul_set_subsetproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- interior_subset_gauge_lt_oneproof · cited by 5
- gauge_add_leproof · cited by 4
- setOfPred_gauge_le_eqproof · cited by 3
- continuousAt_gaugeproof · cited by 2
- gauge_le_one_of_memproof · cited by 2
- setOfPred_gauge_lt_eqproof · cited by 2
- setOfPred_gauge_lt_eq'proof · cited by 2
- tendsto_gauge_nhds_zero_nhdsGEproof · cited by 1