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Definition df-sigagen 31285
Description: Define the sigma-algebra generated by a given collection of sets as the intersection of all sigma-algebra containing that set. (Contributed by Thierry Arnoux, 27-Dec-2016.)
Assertion
Ref Expression
df-sigagen sigaGen = (𝑥 ∈ V ↦ {𝑠 ∈ (sigAlgebra‘ 𝑥) ∣ 𝑥𝑠})
Distinct variable group:   𝑥,𝑠

Detailed syntax breakdown of Definition df-sigagen
StepHypRef Expression
1 csigagen 31284 . 2 class sigaGen
2 vx . . 3 setvar 𝑥
3 cvv 3499 . . 3 class V
42cv 1529 . . . . . 6 class 𝑥
5 vs . . . . . . 7 setvar 𝑠
65cv 1529 . . . . . 6 class 𝑠
74, 6wss 3939 . . . . 5 wff 𝑥𝑠
84cuni 4836 . . . . . 6 class 𝑥
9 csiga 31254 . . . . . 6 class sigAlgebra
108, 9cfv 6351 . . . . 5 class (sigAlgebra‘ 𝑥)
117, 5, 10crab 3146 . . . 4 class {𝑠 ∈ (sigAlgebra‘ 𝑥) ∣ 𝑥𝑠}
1211cint 4873 . . 3 class {𝑠 ∈ (sigAlgebra‘ 𝑥) ∣ 𝑥𝑠}
132, 3, 12cmpt 5142 . 2 class (𝑥 ∈ V ↦ {𝑠 ∈ (sigAlgebra‘ 𝑥) ∣ 𝑥𝑠})
141, 13wceq 1530 1 wff sigaGen = (𝑥 ∈ V ↦ {𝑠 ∈ (sigAlgebra‘ 𝑥) ∣ 𝑥𝑠})
Colors of variables: wff setvar class
This definition is referenced by:  sigagenval  31286  dmsigagen  31290  brsiga  31329
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