in place of D$_{0}$ ( R d$_{x}$ ) . Consider the usual kernel estimator of conditional distribution; typically its limit properties are available under smoothness conditions on the distribution (see, e.g. Li and Racine, 2007). Here the estimator is examined in the space of generalized functions without any restrictions placed on the distribution beyond Assumption 2 (continuity of F$_{x}$ ) . Recall the usual kernel estimator of conditional distribution: where ¯ G is the integral of a kernel function G similar to K that satisfies Assumption 1 on R d$_{y}$ and K satisfies Assumption 1 on R $^{d$_{x}$}$. Sometimes ¯ G is assumed to be the indicator function I ( w > 0) . To simplify exposition we assume that each component of vector x is associated with the same (scalar) bandwidth parameter h ; it is not difficult to generalize to the case of distinct bandwidths. Theorem 3. Suppose that Assumption 1 on the kernel K and either 23 ˆ F$_{y}$$_{|}$$_{x}$ ( x,y ) = Σ ¯ G ( y − y$_{i}$ h$_{y}$ ) K ( x$_{i}$ − x h ) Σ K ( x$_{i}$ − x h ) (16) = 1 $_{n}$Σ ¯ G ( y − y$_{i}$ h$_{y}$ ) 1 h d $_{x}$K ( x$_{i}$ − x h ) ˆ f$_{x}$ ( x ) , (17) 5 Limit properties of kernel estimators of con- ditional distribution in generalized functions