Formal Definition
Let (X, Σ) and (Y, Τ) be measurable spaces, meaning that X and Y are sets equipped with respective sigma algebras Σ and Τ. A function f: X → Y is said to be measurable if f−1(E) ∈ Σ for every E ∈ Τ. The notion of measurability depends on the sigma algebras Σ and Τ. To emphasize this dependency, if f: X → Y is a measurable function, we will write
-
- f: (X, Σ) → (Y, Τ).
Read more about this topic: Measurable Function
Famous quotes containing the words formal and/or definition:
“The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
—Simon Hoggart (b. 1946)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)