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Definition df-ae 27701
Description: Define 'almost everywhere' with regard to a measure  M. A property holds almost everywhere if the measure of the set where it does not hold has measure zero. (Contributed by Thierry Arnoux, 20-Oct-2017.)
Assertion
Ref Expression
df-ae  |- a.e.  =  { <. a ,  m >.  |  ( m `  ( U. dom  m  \  a
) )  =  0 }
Distinct variable group:    m, a

Detailed syntax breakdown of Definition df-ae
StepHypRef Expression
1 cae 27699 . 2  class a.e.
2 vm . . . . . . . . 9  setvar  m
32cv 1373 . . . . . . . 8  class  m
43cdm 4992 . . . . . . 7  class  dom  m
54cuni 4238 . . . . . 6  class  U. dom  m
6 va . . . . . . 7  setvar  a
76cv 1373 . . . . . 6  class  a
85, 7cdif 3466 . . . . 5  class  ( U. dom  m  \  a )
98, 3cfv 5579 . . . 4  class  ( m `
 ( U. dom  m  \  a ) )
10 cc0 9481 . . . 4  class  0
119, 10wceq 1374 . . 3  wff  ( m `
 ( U. dom  m  \  a ) )  =  0
1211, 6, 2copab 4497 . 2  class  { <. a ,  m >.  |  ( m `  ( U. dom  m  \  a ) )  =  0 }
131, 12wceq 1374 1  wff a.e.  =  { <. a ,  m >.  |  ( m `  ( U. dom  m  \  a
) )  =  0 }
Colors of variables: wff setvar class
This definition is referenced by:  relae  27702  brae  27703  braew  27704
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