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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-prob | Structured version Visualization version GIF version |
Description: Define the class of probability measures as the set of measures with total measure 1. (Contributed by Thierry Arnoux, 14-Sep-2016.) |
Ref | Expression |
---|---|
df-prob | ⊢ Prob = {𝑝 ∈ ∪ ran measures ∣ (𝑝‘∪ dom 𝑝) = 1} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cprb 33401 | . 2 class Prob | |
2 | vp | . . . . . . . 8 setvar 𝑝 | |
3 | 2 | cv 1540 | . . . . . . 7 class 𝑝 |
4 | 3 | cdm 5676 | . . . . . 6 class dom 𝑝 |
5 | 4 | cuni 4908 | . . . . 5 class ∪ dom 𝑝 |
6 | 5, 3 | cfv 6543 | . . . 4 class (𝑝‘∪ dom 𝑝) |
7 | c1 11110 | . . . 4 class 1 | |
8 | 6, 7 | wceq 1541 | . . 3 wff (𝑝‘∪ dom 𝑝) = 1 |
9 | cmeas 33188 | . . . . 5 class measures | |
10 | 9 | crn 5677 | . . . 4 class ran measures |
11 | 10 | cuni 4908 | . . 3 class ∪ ran measures |
12 | 8, 2, 11 | crab 3432 | . 2 class {𝑝 ∈ ∪ ran measures ∣ (𝑝‘∪ dom 𝑝) = 1} |
13 | 1, 12 | wceq 1541 | 1 wff Prob = {𝑝 ∈ ∪ ran measures ∣ (𝑝‘∪ dom 𝑝) = 1} |
Colors of variables: wff setvar class |
This definition is referenced by: elprob 33403 |
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