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:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prized—all these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“... 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)