# Infinite Dimensional integral

Is an integral over an infinite dimensional space defined somewhere? For example, does it make sense to think about

$$\lim_{n \to \infty} \int_{\mathbb{R}^n}f_n(\mathbf{x})\,d\mathbf{x}, \quad \mathbf{x} \in \mathbb{R}^n, \quad f_n:\mathbb{R}^n \to \mathbb{R}$$

or is there something similar to this idea?

• Maybe you meant to have $f$ depend on $n$ as well, i.e. have functions $f_n$, each defined on $\mathbb R^n$. – mickep Oct 11 '17 at 6:43
• You are right, thanks. I'll update the question. – Student Oct 11 '17 at 6:44