Exercise 1, § 1

Let T be a set and p an encumbrance on T. For every subset A of T, set $p(A) = p(\varphi_A)$. a) $p(A) \leq p(B)$ when A is contained in B. b) For every sequence $(A_n)$, finite or not, of subsets of T, $p\left( \bigcup_n A_n \right) \leq \sum_n p(A_n)$. c) For every increasing sequence $(A_n)_{n \geq 1}$ of subsets of T, $p\left( \bigcup_n A_n \right) = \lim_{n \to \infty} p(A_n)$.