Join Nostr
2025-10-29 19:58:00 UTC

julesh on Nostr: I have a probably-basic analysis question Nonnegative numbers satisfy the inequality ...

I have a probably-basic analysis question

Nonnegative numbers satisfy the inequality
𝑥₁𝑦₁ + 𝑥₂𝑦₂ ≤ (𝑥₁ + 𝑥₂)(𝑦₁ + 𝑦₂)
Do nonnegative functions satisfy the corresponding inequality
∫ 𝑓𝑔 ≤ (∫ 𝑓)(∫ 𝑔) ?

(In case it helps I think I can also guarantee that the integrals are all finite)