Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-voln | Structured version Visualization version GIF version |
Description: Define the Lebesgue measure for the space of multidimensional real numbers. The cardinality of 𝑥 is the dimension of the space modeled. Definition 115C of [Fremlin1] p. 30. (Contributed by Glauco Siliprandi, 11-Oct-2020.) |
Ref | Expression |
---|---|
df-voln | ⊢ voln = (𝑥 ∈ Fin ↦ ((voln*‘𝑥) ↾ (CaraGen‘(voln*‘𝑥)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvoln 43602 | . 2 class voln | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cfn 8548 | . . 3 class Fin | |
4 | 2 | cv 1541 | . . . . 5 class 𝑥 |
5 | covoln 43600 | . . . . 5 class voln* | |
6 | 4, 5 | cfv 6333 | . . . 4 class (voln*‘𝑥) |
7 | ccaragen 43555 | . . . . 5 class CaraGen | |
8 | 6, 7 | cfv 6333 | . . . 4 class (CaraGen‘(voln*‘𝑥)) |
9 | 6, 8 | cres 5521 | . . 3 class ((voln*‘𝑥) ↾ (CaraGen‘(voln*‘𝑥))) |
10 | 2, 3, 9 | cmpt 5107 | . 2 class (𝑥 ∈ Fin ↦ ((voln*‘𝑥) ↾ (CaraGen‘(voln*‘𝑥)))) |
11 | 1, 10 | wceq 1542 | 1 wff voln = (𝑥 ∈ Fin ↦ ((voln*‘𝑥) ↾ (CaraGen‘(voln*‘𝑥)))) |
Colors of variables: wff setvar class |
This definition is referenced by: vonval 43604 |
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