exists for all but at most

countably many [epsilon] > 0.

Eigenvalue problem (107) has

countably many solutions ([w.sub.i], [[lambda].sub.i]) such that

(ii) the function [phi] has preimages of cardinality one except at

countably many points of T.

Indeed by a

countably many operations uunion and intersection" on the union {[A.sub.n]}[union]{[A.sub.n]}, one may construct A.

Since only

countably many functions are involved in the proofs of the above theorems and as Bochner integrable functions have u-finite support, Theorem 2.2 and Theorem 2.3 are valid for any complete measure space.

He suggested to consider words with not just one but

countably many additional unary operations.

as this holds for each of the

countably many pairs (p, k) with p : E [right arrow] Q and k > 1, the thesis follows.

It follows that elements u(t) of [U.sup.p](I) are right-continuous, have left limits everywhere (including at b) and at most

countably many discontinuities.

A fibre can be defined as a curve of class [C.sup.1] with finite length and a system of fibres as the union of at most

countably many fibres that can have only the endpoints in common (see Stoyan et al.

184), while, in every formal system, only

countably many are available.

(1970): "Markets with

Countably Many Commodities" International Economic Review, 11(3), 369-377.