Integral solution needed containing indicator function

Question

I want to solve the following integral $$\int_{\mathbb{R}^2}\mathbb{1}(x\in C) \, dx$$ where $\mathbb{1}$ is the indicator function and $C$ is a subset of Borel $\sigma$ algebra $B(\mathbb{R}^2)$. My above integral is similar to the integral present in Lemma 1 of https://arxiv.org/pdf/1306.6122v1.pdf . I do not know how to solve this integral. Please help in solving this.