Sei X ⊂⊂ R n , ( f ν ) ν ∈ N : X → stetig R {\displaystyle X\subset \subset {{\mathbb {R} }^{n}},\quad {{\left({{f}_{\nu }}\right)}_{\nu \in \mathbb {N} }}:X{\underset {\text{stetig}}{\mathop {\to } }}\,\mathbb {R} } und es gelte 1. f ν ( x ) ≤ f ν + 1 ( x ) ∀ ν ∈ N , ∀ x ∈ X {\displaystyle {{f}_{\nu }}\left(x\right)\leq {{f}_{\nu +1}}\left(x\right)\quad \forall \nu \in \mathbb {N} ,\forall x\in X} 2. ∃ f ( x ) := sup ν ∈ N f ν ( x ) ∀ x ∈ X {\displaystyle \exists f\left(x\right):={\underset {\nu \in \mathbb {N} }{\mathop {\sup } }}\,{{f}_{\nu }}\left(x\right)\forall x\in X}
