Approximating Bochner integrals by Riemann sums
نویسندگان
چکیده
منابع مشابه
4: Riemann Sums, Riemann Integrals, Fundamental Theorem of Calculus
Proposition 1.3. Let X be a subset of R, let x0 be a limit point of X, let f : X → R be a function, and let L be a real number. Then the following two statements are equivalent. • f is differentiable at x0 on X with derivative L. • For every ε > 0, there exists a δ = δ(ε) > 0 such that, if x ∈ X satisfies |x− x0| < δ, then |f(x)− [f(x0) + L(x− x0)]| ≤ ε |x− x0| . Corollary 1.4 (Mean Value Theor...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2002
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(02)80005-2