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Mirrors > Home > MPE Home > Th. List > df-vol | Structured version Visualization version Unicode version |
Description: Define the Lebesgue measure, which is just the outer measure with a peculiar domain of definition. The property of being Lebesgue-measurable can be expressed as . (Contributed by Mario Carneiro, 17-Mar-2014.) |
Ref | Expression |
---|---|
df-vol |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvol 23232 | . 2 | |
2 | covol 23231 | . . 3 | |
3 | vy | . . . . . . . 8 | |
4 | 3 | cv 1482 | . . . . . . 7 |
5 | 4, 2 | cfv 5888 | . . . . . 6 |
6 | vx | . . . . . . . . . 10 | |
7 | 6 | cv 1482 | . . . . . . . . 9 |
8 | 4, 7 | cin 3573 | . . . . . . . 8 |
9 | 8, 2 | cfv 5888 | . . . . . . 7 |
10 | 4, 7 | cdif 3571 | . . . . . . . 8 |
11 | 10, 2 | cfv 5888 | . . . . . . 7 |
12 | caddc 9939 | . . . . . . 7 | |
13 | 9, 11, 12 | co 6650 | . . . . . 6 |
14 | 5, 13 | wceq 1483 | . . . . 5 |
15 | 2 | ccnv 5113 | . . . . . 6 |
16 | cr 9935 | . . . . . 6 | |
17 | 15, 16 | cima 5117 | . . . . 5 |
18 | 14, 3, 17 | wral 2912 | . . . 4 |
19 | 18, 6 | cab 2608 | . . 3 |
20 | 2, 19 | cres 5116 | . 2 |
21 | 1, 20 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: ismbl 23294 volres 23296 |
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