Pointwise

Definition

$X$, $M$ then $f:X\to \mathbb{C}$ measure form an algebra under pointwise operations:
$(f+g)(x)=f(x)+g(x)$
$(f\circ g)(x)=f(x)\times g(x)$

Example

$(f+g)(x)=f(x)+g(x)$
The plus part of this operation is the pointwise part