Measurable function
Set
| context | ⟨X,ΣX⟩∈MeasurableSpace(X) |
| context | ⟨Y,ΣY⟩∈MeasurableSpace(Y) |
| postulate | f∈Measurable(X,Y) |
| context | f:X→Y |
| y∈ΣY |
| postulate | f−1(y)∈ΣX |
Discussion
This is very similar to the definition of continuous function.
People write f:⟨X,ΣX⟩→⟨Y,ΣY⟩ to point out the function is measurable, although I'd say that's abuse of language.
Reference
Wikipedia: Sigma-algebra
Parents
Subset of
Context
