集合函数
単調減少列 Aj で f(A1) < ∞ なるものに対して f ( ⋂ i ∈ N A i ) = inf i ∈ N f ( A i ) ( if ⋂ j ∈ N A j ∈ C ) . {\displaystyle f(\bigcap _{i\in \mathbb {N} }A_{i})=\inf _{i\in \mathbb {N} }f(A_{i})\quad ({\text{if }}\bigcap _{j\in \mathbb {N} }A_{j}\in {\mathcal {C}}).}
f ( ⋃ j ∈ N A j ) = ∑ j ∈ N f ( A j ) ( if [ i ≠ j ⟹ A i ∩ A j = ∅ ] ∧ ⋃ j ∈ N A j ∈ C ) . {\displaystyle f(\bigcup _{j\in \mathbb {N} }A_{j})=\sum _{j\in \mathbb {N} }f(A_{j})\quad ({\text{if }}[i\neq j\implies A_{i}\cap A_{j}=\emptyset ]\land \bigcup _{j\in \mathbb {N} }A_{j}\in {\mathcal {C}}).}