I have problems understanding the proof of this lemma:
$$\lambda \in \Lambda (m, n), \ \ \text{this means that it is an increasing function} \ \ \lambda: \{1,2,...,m\} \rightarrow \{1,...,n\}, \ \ \text{so} \ \ \lambda(1) < ... < \lambda(m)$$
$$p_{\lambda} : \mathbb{R}^m \ni (x_1, ..., x_m)...