Description: The Lebesgue outer measure of a set is an extended real. (Contributed by Glauco Siliprandi, 11-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ovnxrcl.1 | ⊢ ( 𝜑 → 𝑋 ∈ Fin ) | |
ovnxrcl.2 | ⊢ ( 𝜑 → 𝐴 ⊆ ( ℝ ↑m 𝑋 ) ) | ||
Assertion | ovnxrcl | ⊢ ( 𝜑 → ( ( voln* ‘ 𝑋 ) ‘ 𝐴 ) ∈ ℝ* ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovnxrcl.1 | ⊢ ( 𝜑 → 𝑋 ∈ Fin ) | |
2 | ovnxrcl.2 | ⊢ ( 𝜑 → 𝐴 ⊆ ( ℝ ↑m 𝑋 ) ) | |
3 | iccssxr | ⊢ ( 0 [,] +∞ ) ⊆ ℝ* | |
4 | 1 2 | ovncl | ⊢ ( 𝜑 → ( ( voln* ‘ 𝑋 ) ‘ 𝐴 ) ∈ ( 0 [,] +∞ ) ) |
5 | 3 4 | sselid | ⊢ ( 𝜑 → ( ( voln* ‘ 𝑋 ) ‘ 𝐴 ) ∈ ℝ* ) |