Nuprl Lemma : rv-unbounded_wf
∀[p:FinProbSpace]. ∀[f:ℕ ─→ ℕ]. ∀[X:n:ℕ ─→ RandomVariable(p;f[n])]. ((X[n]─→∞ as n─→∞) ∈ (ℕ ─→ Outcome) ─→ ℙ)
Proof
Definitions occuring in Statement :
rv-unbounded: (X[n]─→∞ as n─→∞),
random-variable: RandomVariable(p;n),
p-outcome: Outcome,
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,
rationals_wf,
exists_wf,
le_wf,
Error :qle_wf,
random-variable_wf,
subtype_rel_dep_function,
p-outcome_wf,
int_seg_wf,
nat_wf,
length_wf,
int_seg_subtype-nat,
false_wf,
finite-prob-space_wf
\mforall{}[p:FinProbSpace]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[X:n:\mBbbN{} {}\mrightarrow{} RandomVariable(p;f[n])].
((X[n]{}\mrightarrow{}\minfty{} as n{}\mrightarrow{}\minfty{}) \mmember{} (\mBbbN{} {}\mrightarrow{} Outcome) {}\mrightarrow{} \mBbbP{})
Date html generated:
2015_07_17-AM-08_01_25
Last ObjectModification:
2015_01_27-AM-11_21_55
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