Theorems · Theorem · functional analysis
HasSum.enorm_le_of_bounded
∀ {ι : Type u_1} {ε : Type u_5} [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddCommMonoid ε] {f : ι → ε}
{g : ι → ENNReal} {a : ε} {b : ENNReal}, HasSum f a → HasSum g b → (∀ (i : ι), ‖f i‖ₑ ≤ g i) → ‖a‖ₑ ≤ b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENorm.enormstatement and proof · cited by 715
- HasSumstatement and proof · cited by 518
- ESeminormedAddCommMonoidstatement and proof · cited by 21
- le_of_tendsto_of_tendsto'proof · cited by 19
- Filter.Tendsto.enormproof · cited by 2
- enorm_sum_le_of_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- tsum_of_enorm_boundedproof · cited by 1