Theorems · Theorem · functional analysis
lp.norm_rpow_eq_tsum
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)],
0 < p.toReal → ∀ (f : ↥(lp E p)), ‖f‖ ^ p.toReal = ∑' (i : α), ‖↑f i‖ ^ p.toReal- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement and proof · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- one_mulproof · cited by 2,841
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- one_ne_zeroproof · cited by 885
- ENNReal.toRealstatement and proof · cited by 859
- norm_nonnegproof · cited by 725
- ne_of_gtproof · cited by 637
Cited by3
Results whose statement or proof uses this declaration.
- lp.hasSum_normproof · cited by 9
- lp.sum_rpow_le_norm_rpowproof · cited by 2
- lp.norm_le_of_tsum_leproof · cited by 1