In a probability space (Ω,σ,P), for α ⊂ σ a sub-σ field, in general the best approximation in L∞ by elements of L∞(α) has not a unique solution. For the election between these, we prove the convergence P-almost surely of the conditional r-means, when r → ∞, to one solution, which we call conditional mid-range. This is characterized for each ω ∈ Ω by the mid-range, of one regular conditional distribution Q(ω, ·).
@article{urn:eudml:doc:40714,
title = {Semi-recorrido condicionado (expresi\'on asint\'otica de la r-esperanza condicionada).},
journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa},
volume = {34},
year = {1983},
pages = {55-60},
zbl = {0734.60002},
mrnumber = {MR0829664},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40714}
}
Cuesta Albertos, Juan Antonio; Matrán Bea, Carlos. Semi-recorrido condicionado (expresión asintótica de la r-esperanza condicionada).. Trabajos de Estadística e Investigación Operativa, Tome 34 (1983) pp. 55-60. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40714/