Nuprl Lemma : rv-identically-distributed_wf
∀[p:FinProbSpace]. ∀[f:ℕ ─→ ℕ]. ∀[X:n:ℕ ─→ RandomVariable(p;f[n])]. (rv-identically-distributed(p;n.f[n];n.X[n]) ∈ ℙ)
Proof
Definitions occuring in Statement :
rv-identically-distributed: rv-identically-distributed(p;n.f[n];i.X[i]),
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x]
Lemmas :
all_wf,
nat_wf,
rationals_wf,
expectation_wf,
rv-compose_wf,
qmul_wf,
random-variable_wf,
finite-prob-space_wf
\mforall{}[p:FinProbSpace]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[X:n:\mBbbN{} {}\mrightarrow{} RandomVariable(p;f[n])].
(rv-identically-distributed(p;n.f[n];n.X[n]) \mmember{} \mBbbP{})
Date html generated:
2015_07_17-AM-08_01_59
Last ObjectModification:
2015_01_27-AM-11_21_50
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