Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the approximation or integration of functions defined on $D_d\subset {\mathbb{R}}^d$ and only assume that $D_d$ is a bounded Lipschitz domain. Some results are even more general. We study three different concepts to measure the complexity: order of convergence, asymptotic constant, and explicit uniform bounds, i.e., bounds that hold for all $n$ (number of pieces of information) and all (normalized) domains. It is known for many problems that the order of convergence of optimal algorithms does not depend on the domain $D_d\subset {\mathbb{R}}^d$. We present examples for which the following statements are true:

1. Also the asymptotic constant does not depend on the shape of $D_d$ or the imposed boundary values, it only depends on the volume of the domain.

2. There are explicit and uniform lower (or upper, respectively) bounds for the error that are only slightly smaller (or larger, respectively) than the asymptotic error bound.

对于在非常简单的域（例如立方体，圆环或球体）上定义的函数，经常会证明数值分析和基于信息的复杂性中的错误界限和复杂性界限。我们研究关于定义在函数上的近似或积分的最佳误差范围$d_d\subset {\mathbb{[R}}^d$ 并仅假设 $d_d$是有界的Lipschitz域。一些结果甚至更一般。我们研究了三种不同的概念来衡量复杂性：收敛顺序，渐近常数和显式统一边界，即适用于所有人的边界$ñ$（信息条数）和所有（规范化）域。对于许多问题，众所周知，最佳算法的收敛顺序不取决于域$d_d\subset {\mathbb{[R}}^d$。我们提供了以下陈述正确的示例：

1.渐近常数也不取决于 $d_d$ 或强加的边界值，它仅取决于域的体积。

2.对于误差，有明确且统一的下界（或上限），它们仅比渐近误差界限略小（或分别大一点）。