Conditional Distributions as Derivatives

Pfanzagl, P.

Pfanzagl, P.

Ann. Probab., Tome 7 (1979) no. 6, p. 1046-1050 / Harvested from Project Euclid

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Résumé

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/