Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-vol Unicode version

Definition df-vol 18825
 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.)
Assertion
Ref Expression
df-vol
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-vol
StepHypRef Expression
1 cvol 18823 . 2
2 covol 18822 . . 3
3 vy . . . . . . . 8
43cv 1622 . . . . . . 7
54, 2cfv 5255 . . . . . 6
6 vx . . . . . . . . . 10
76cv 1622 . . . . . . . . 9
84, 7cin 3151 . . . . . . . 8
98, 2cfv 5255 . . . . . . 7
104, 7cdif 3149 . . . . . . . 8
1110, 2cfv 5255 . . . . . . 7
12 caddc 8740 . . . . . . 7
139, 11, 12co 5858 . . . . . 6
145, 13wceq 1623 . . . . 5
152ccnv 4688 . . . . . 6
16 cr 8736 . . . . . 6
1715, 16cima 4692 . . . . 5
1814, 3, 17wral 2543 . . . 4
1918, 6cab 2269 . . 3
202, 19cres 4691 . 2
211, 20wceq 1623 1
 Colors of variables: wff set class This definition is referenced by:  ismbl  18885  volres  18887
 Copyright terms: Public domain W3C validator