Theorems · Theorem · functional analysis
egauge_le_of_smul_mem
∀ {𝕜 : Type u_1} [inst : NormedDivisionRing 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] {c : 𝕜}
{s : Set E} {x : E}, c • x ∈ s → egauge 𝕜 s x ≤ ‖c‖ₑ⁻¹If c • x ∈ s, then egauge 𝕜 s x is at most ‖c‖ₑ⁻¹.
See also egauge_le_of_smul_mem_of_ne.
- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- ENNRealstatement · cited by 9,879
- LE.le.transproof · cited by 3,151
- eq_or_neproof · cited by 1,117
- ENorm.enormstatement · cited by 715
- NormedDivisionRingstatement and proof · cited by 360
- egaugestatement and proof · cited by 75
- enorm_zeroproof · cited by 44
- ENNReal.inv_zeroproof · cited by 37
- ENNReal.coe_inv_leproof · cited by 3
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