Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 556–557 页 · Chapter IX，Section 1「Infinite-dimensional Representations of Compact Groups」，章首约定、连续性约定及左正则表示（省略中间的说明与证明）
Throughout this chapter, $G$ will denote a compact group, and $dx$ will denote a two-sided Haar measure on $G$ of total mass $1$. […] A unitary representation of $G$ on the complex Hilbert space $V$ is a homomorphism of $G$ into the group of unitary operators on $V$ such that a certain continuity property holds. […] The continuity property we choose is that the group action $G\times V\to V$, given by $g\times v\mapsto\Phi(g)v$, is continuous. […] With this definition of continuity in place, an example of a unitary representation is the left-regular representation of $G$ on the complex Hilbert space $L^2(G)$, given by $(l(g)f)(x)=f(g^{-1}x)$.