Definition df-prob 30470

Description: Define the class of probability measures as the set of measures with total measure 1. (Contributed by Thierry Arnoux, 14-Sep-2016.)

Assertion

Ref	Expression
df-prob	|- Prob = { p e. U. ran measures | ( p ` U. dom p ) = 1 }

Detailed syntax breakdown of Definition df-prob

Step	Hyp	Ref	Expression
1		cprb 30469	. 2 class Prob
2		vp	. . . . . . . 8 setvar p
3	2	cv 1482	. . . . . . 7 class p
4	3	cdm 5114	. . . . . 6 class dom p
5	4	cuni 4436	. . . . 5 class U. dom p
6	5, 3	cfv 5888	. . . 4 class ( p ` U. dom p )
7		c1 9937	. . . 4 class 1
8	6, 7	wceq 1483	. . 3 wff ( p ` U. dom p ) = 1
9		cmeas 30258	. . . . 5 class measures
10	9	crn 5115	. . . 4 class ran measures
11	10	cuni 4436	. . 3 class U. ran measures
12	8, 2, 11	crab 2916	. 2 class { p e. U. ran measures | ( p ` U. dom p ) = 1 }
13	1, 12	wceq 1483	1 wff Prob = { p e. U. ran measures | ( p ` U. dom p ) = 1 }

This definition is referenced by:  elprob  30471