Nuprl Lemma : nullset-monotone
∀p:FinProbSpace. ∀[P,Q:(ℕ ─→ Outcome) ─→ ℙ]. ((∀s:ℕ ─→ Outcome. (Q[s] ⇒ P[s])) ⇒ nullset(p;P) ⇒ nullset(p;Q))
Proof
Definitions occuring in Statement :
nullset: nullset(p;S),
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x]
Lemmas :
all_wf,
p-open-member_wf,
p-measure-le_wf,
set_wf,
rationals_wf,
Error :qless_wf,
int-subtype-rationals,
nullset_wf,
nat_wf,
p-outcome_wf,
finite-prob-space_wf
\mforall{}p:FinProbSpace
\mforall{}[P,Q:(\mBbbN{} {}\mrightarrow{} Outcome) {}\mrightarrow{} \mBbbP{}]. ((\mforall{}s:\mBbbN{} {}\mrightarrow{} Outcome. (Q[s] {}\mRightarrow{} P[s])) {}\mRightarrow{} nullset(p;P) {}\mRightarrow{} nullset(p;Q))
Date html generated:
2015_07_17-AM-08_01_22
Last ObjectModification:
2015_01_27-AM-11_21_48
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