ACIT4330-Page/content/Definitions/Terminology/Pointwise.md

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