Theorems · Theorem · functional analysis

lp.norm_eq_tsum_rpow

∀ {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‖ = (∑' (i : α), ‖↑f i‖ ^ p.toReal) ^ (1 / p.toReal)

Defined in

Mathlib.Analysis.Normed.Lp.lpSpace

Cited by

7 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup