Description: Simple functions are measurable. (Contributed by Mario Carneiro, 18-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | i1fmbf | ⊢ ( 𝐹 ∈ dom ∫1 → 𝐹 ∈ MblFn ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isi1f | ⊢ ( 𝐹 ∈ dom ∫1 ↔ ( 𝐹 ∈ MblFn ∧ ( 𝐹 : ℝ ⟶ ℝ ∧ ran 𝐹 ∈ Fin ∧ ( vol ‘ ( ◡ 𝐹 “ ( ℝ ∖ { 0 } ) ) ) ∈ ℝ ) ) ) | |
2 | 1 | simplbi | ⊢ ( 𝐹 ∈ dom ∫1 → 𝐹 ∈ MblFn ) |