Users' Mathboxes Mathbox for Thierry Arnoux < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-sx Structured version   Unicode version

Definition df-sx 27786
Description: Define the product sigma-algebra operation, analogue to df-tx 19791. (Contributed by Thierry Arnoux, 1-Jun-2017.)
Assertion
Ref Expression
df-sx  |- ×s  =  ( s  e.  _V ,  t  e. 
_V  |->  (sigaGen `  ran  ( x  e.  s ,  y  e.  t  |->  ( x  X.  y ) ) ) )
Distinct variable group:    t, s, x, y

Detailed syntax breakdown of Definition df-sx
StepHypRef Expression
1 csx 27785 . 2  class ×s
2 vs . . 3  setvar  s
3 vt . . 3  setvar  t
4 cvv 3106 . . 3  class  _V
5 vx . . . . . 6  setvar  x
6 vy . . . . . 6  setvar  y
72cv 1373 . . . . . 6  class  s
83cv 1373 . . . . . 6  class  t
95cv 1373 . . . . . . 7  class  x
106cv 1373 . . . . . . 7  class  y
119, 10cxp 4990 . . . . . 6  class  ( x  X.  y )
125, 6, 7, 8, 11cmpt2 6277 . . . . 5  class  ( x  e.  s ,  y  e.  t  |->  ( x  X.  y ) )
1312crn 4993 . . . 4  class  ran  (
x  e.  s ,  y  e.  t  |->  ( x  X.  y ) )
14 csigagen 27764 . . . 4  class sigaGen
1513, 14cfv 5579 . . 3  class  (sigaGen `  ran  ( x  e.  s ,  y  e.  t  |->  ( x  X.  y
) ) )
162, 3, 4, 4, 15cmpt2 6277 . 2  class  ( s  e.  _V ,  t  e.  _V  |->  (sigaGen `  ran  ( x  e.  s ,  y  e.  t  |->  ( x  X.  y
) ) ) )
171, 16wceq 1374 1  wff ×s  =  ( s  e.  _V ,  t  e. 
_V  |->  (sigaGen `  ran  ( x  e.  s ,  y  e.  t  |->  ( x  X.  y ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  sxval  27787
  Copyright terms: Public domain W3C validator