![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > df-vol | Structured 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 ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
df-vol |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cvol 21082 |
. 2
![]() ![]() | |
2 | covol 21081 |
. . 3
![]() ![]() ![]() | |
3 | vy |
. . . . . . . 8
![]() ![]() | |
4 | 3 | cv 1369 |
. . . . . . 7
![]() ![]() |
5 | 4, 2 | cfv 5529 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | vx |
. . . . . . . . . 10
![]() ![]() | |
7 | 6 | cv 1369 |
. . . . . . . . 9
![]() ![]() |
8 | 4, 7 | cin 3438 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
9 | 8, 2 | cfv 5529 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 4, 7 | cdif 3436 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
11 | 10, 2 | cfv 5529 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | caddc 9399 |
. . . . . . 7
![]() ![]() | |
13 | 9, 11, 12 | co 6203 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 5, 13 | wceq 1370 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 2 | ccnv 4950 |
. . . . . 6
![]() ![]() ![]() ![]() |
16 | cr 9395 |
. . . . . 6
![]() ![]() | |
17 | 15, 16 | cima 4954 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 14, 3, 17 | wral 2799 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 18, 6 | cab 2439 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 2, 19 | cres 4953 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 1, 20 | wceq 1370 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: ismbl 21144 volres 21146 |
Copyright terms: Public domain | W3C validator |