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.