Conditional Distributions as Derivatives
Pfanzagl, P.
Ann. Probab., Tome 7 (1979) no. 6, p. 1046-1050 / Harvested from Project Euclid
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Let $(X, \mathscr{a}, P)$ be a probability space, $Y$ a complete separable metric space, $Z$ a separable metric space, and $s: X\rightarrow Y, t: X\rightarrow Z$ Borel measurable functions. Then the weak limit of $P\{s \in B, t \in C\}/P\{t \in C\}$ for $C\downarrow\{z\}$ exists for $P-\mathrm{a.a.} z \in Z$, and is a regular conditional distribution of $s$, given $t$.
Publié le : 1979-12-14
Classification:  Conditional distributions,  differentiation of measures,  60A10,  28A15 
@article{1176994897,
     author = {Pfanzagl, P.},
     title = {Conditional Distributions as Derivatives},
     journal = {Ann. Probab.},
     volume = {7},
     number = {6},
     year = {1979},
     pages = { 1046-1050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994897}
}

Pfanzagl, P. Conditional Distributions as Derivatives. Ann. Probab., Tome 7 (1979) no. 6, pp.  1046-1050. http://gdmltest.u-ga.fr/item/1176994897/