Theorems · Theorem · real analysis

NNReal.inner_le_Lp_mul_Lq_tsum

∀ {ι : Type u} {f g : ι → NNReal} {p q : ℝ},
  p.HolderConjugate q →
    (Summable fun i => f i ^ p) →
      (Summable fun i => g i ^ q) →
        ∑' (i : ι), f i * g i ≤ (∑' (i : ι), f i ^ p) ^ (1 / p) * (∑' (i : ι), g i ^ q) ^ (1 / q)

Defined in: Mathlib.Analysis.MeanInequalities
Cited by: 1 results in Mathlib
Foundations: Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

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Realstatement and proof · cited by 25,697
NNRealstatement and proof · cited by 4,310
SummationFilter.unconditionalstatement and proof · cited by 2,068
tsumstatement · cited by 1,148
Summablestatement and proof · cited by 778
Real.HolderConjugatestatement and proof · cited by 78
NNReal.summable_and_inner_le_Lp_mul_Lq_tsumproof · cited by 3

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NNReal.inner_le_Lp_mul_Lq_tsum'proof · cited by 0