Nuprl Lemma : slln-lemma3 11,40

p:FinProbSpace, f:(), X:(n:RandomVariable(p;f(n))), sk:.
(n:i:{0..n}. f(i) < f(n))
 (n:.
 E(f(n);X(n)) = 0   & E(f(n);(x.x * x) o X(n)) = s & E(f(n);(x.(x * x) * x * x) o X(n)) = k)
 (n:i:{0..n}. rv-disjoint(p;f(n);X(i);X(n)))
 nullset(p;s.q:. (0 < q & (n:m:. ((n < m) & q  | i < m. (1/m) * (X(i)(s))|)))) 
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Definitionsx:AB(x), , RandomVariable(p;n), x(s), P  Q, {i..j}, P & Q, t  T, , Top, S  T, i  j < k, xt(x), if b then t else f fi , tt, ff, A, t  ...$L, rv-partial-sum(n;i.X(i)), rv-const(a), A  B, False, T, True, P  Q, P  Q, r * s, (i = j), r < s, r + s, a < b, a <p b, b, a < b, p  q, x f y, , t.2, goset, gset, , t.1, <+>, q_le(r;s), p q, qpositive(r), r - s, i <z j, b, qeq(r;s), (x.F(x)) o X, r  s, q*X, X  Y, a  b, A c B, SQType(T), {T}, Outcome, , (X(n) as n), x:AB(x), P  Q, suptype(ST), a  b, , a  b  T , (r/s), a  j < bE(j), (ri  k < jE(k), <+*>,  lb  i < ubE(i), r+gp, (op,idlb  i < ubE(i), *, e, +r, 0, Y, 1/r, FinProbSpace, , Unit, Dec(P), SqStable(P),
Lemmasslln-lemma2, nat wf, int seg wf, rv-disjoint wf, length wf nat, top wf, rationals wf, le wf, random-variable wf, subtype rel function, expectation wf, int inc rationals, rv-compose wf, qmul wf, finite-prob-space wf, rv-partial-sum wf, eq int wf, bool wf, iff transitivity, assert wf, eqtt to assert, assert of eq int, rv-const wf, bnot wf, not wf, eqff to assert, assert of bnot, not functionality wrt iff, rv-scale wf, qdiv wf, int-rational, int-eq-in-rationals, qle wf, squash wf, true wf, p-outcome wf, qsum wf, sum unroll base q, expectation-rv-const, qless wf, qadd wf, qadd preserves qless, qadd comm q, qadd ac 1 q, qinverse q, mon ident q, rv-partial-sum-monotone, q-square-non-neg, bounded-expectation, qless transitivity 1 qorder, decidable int equal, qle weakening eq qorder, rv-le wf, int nzero-rational, nat plus inc int nzero, false wf, nullset-monotone, rv-unbounded wf, qabs wf, q-not-limit-zero-diverges-2, qmul-positive, qmul preserves qle, qless transitivity 2 qorder, qmul comm qrng, qle transitivity qorder, prod sum l q, qsum-non-neg2, qle functionality wrt implies, nat plus wf, sq stable from decidable, decidable qle, qabs-squared, sum split q, qadd preserves qle, qadd inv assoc q, nequal wf, nat plus inc, sum unroll lo q, qadd ident

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