Description: A real-valued random variable is a function. (Contributed by Thierry Arnoux, 25-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | isrrvv.1 | |- ( ph -> P e. Prob ) |
|
rrvvf.1 | |- ( ph -> X e. ( rRndVar ` P ) ) |
||
Assertion | rrvvf | |- ( ph -> X : U. dom P --> RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isrrvv.1 | |- ( ph -> P e. Prob ) |
|
2 | rrvvf.1 | |- ( ph -> X e. ( rRndVar ` P ) ) |
|
3 | 1 | isrrvv | |- ( ph -> ( X e. ( rRndVar ` P ) <-> ( X : U. dom P --> RR /\ A. y e. BrSiga ( `' X " y ) e. dom P ) ) ) |
4 | 2 3 | mpbid | |- ( ph -> ( X : U. dom P --> RR /\ A. y e. BrSiga ( `' X " y ) e. dom P ) ) |
5 | 4 | simpld | |- ( ph -> X : U. dom P --> RR ) |