Theorems · Theorem · functional analysis
mem_emetric_ball_zero_iff
Deprecated since 2026-01-24Use mem_eball_zero_iff instead.
∀ {E : Type u_5} [inst : SeminormedAddGroup E] {a : E} {r : ENNReal}, a ∈ Metric.eball 0 r ↔ ‖a‖ₑ < rAlias of mem_eball_zero_iff.
- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- ENorm.enormstatement · cited by 715
- SeminormedAddGroupstatement · cited by 331
- Metric.eballstatement · cited by 294
- mem_eball_zero_iffproof · cited by 8
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