Theorems · Theorem · harmonic analysis
span_fourierLp_closure_eq_top
∀ {T : ℝ} [hT : Fact (0 < T)] {p : ENNReal} [inst : Fact (1 ≤ p)],
p ≠ ⊤ → (Submodule.span ℂ (Set.range (fourierLp p))).topologicalClosure = ⊤For each 1 ≤ p < ∞, the linear span of the monomials fourier n is dense in
Lp ℂ p haarAddCircle.
- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 237 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- Semiringproof · cited by 13,802
- AddCommMonoidproof · cited by 12,281
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Complexstatement and proof · cited by 5,565
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