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
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- f: (X, Σ) → (Y, Τ).
Read more about this topic: Measurable Function
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