Note that the function space is compact with respect to pointwise convergence by Tychonov's theorem.
Expressed in graph theoretical terms, part (a) of the following result shows that the Doob-Martin convergence associated with the uniform attachment graphs is the same as pointwise convergence of the adjacency matrices [M.
The result follows from the compactness of G and the pointwise convergence
The mathematicians investigate the pointwise convergence
of weighted averages linked to averages along cubes, divergent ergodic averages along the squares, the one-sided ergodic Hilbert transform, deterministic walks in Markov environments with constant rigidity, limit theorems for sequential expanding dynamical systems, and random Fourier-Stieltjes transforms.
We will show similar results for the pointwise convergence
p]-norm and pointwise convergence
of this integral.
We show that the convergence of Bayesian estimators comes directly from our first result, the pointwise convergence of the likelihood.
It is important to notice that proposition 5 shows only pointwise convergence of the likelihood function.
The function from the infinite dimensional vectors with the topology of pointwise convergence
to the sum of moduli of their components is discontinuous, its type of discontinuity being nearer to the intuitive idea of unboundedness than to that of 'jumps' in the graph.
A mapping t : L [right arrow] hom(Y, X) which is continuous for the pointwise convergence in hom(Y, X)
A mapping t : L [right arrow] hom([gamma], X) which is continuous for the pointwise convergence in hom(Y, X)
1), the pointwise convergence
for u is uniform across the entire domain.