On an Inequality of Peano(1)
James S. Muldowney · Canadian Mathematical Bulletin · 1973
Let f be a real valued function on an open subset of R2. It is assumed that f satisfies Carathéodory's conditions: f (t,x) is continuous in x for each t, Lebesgue measurable in t for each x and there is a locally integrable function m(t) such that |f(t, x)| ≤ m(t) uniformly in x. A proof will be given of the following theorem.