Nuprl Lemma : slln-lemma4 11,40

p:FinProbSpace, f:(), X:(n:RandomVariable(p;f(n))).
rv-iid(p;n.f(n);n.X(n))
 (E(f(0);X(0)) = 0  )
 nullset(p;s.q:. (0 < q & (n:m:. ((n < m) & q  | i < m. (1/m) * (X(i)(s))|)))) 
latex


Definitionst  T, x:AB(x), A  B, , {x:AB(x)} , FinProbSpace, x:AB(x), measure(C q, s  C, nullset(p;S), s = t, a < b, rv-disjoint(p;n;X;Y), , x:A  B(x), P & Q, i  j < k, {i..j}, Void, P  Q, False, A, <ab>, , A c B, f(a), xt(x), rv-identically-distributed(p;n.f(n);i.X(i)), rv-iid(p;n.f(n);i.X(i)), , r < s, r  s, x:AB(x), RandomVariable(p;n), Type, #$n, x(s), r * s, (x.F(x)) o X, E(n;F)
Lemmasslln-lemma3, finite-prob-space wf, random-variable wf, int inc rationals, rv-iid wf, nat wf, int-rational, expectation wf, rv-compose wf, qmul wf, rationals wf, le wf

origin