Sentence examples for most countable number from inspiring English sources

Using this method, we shall prove that a right regulated mapping has at most countable number of discontinuities, and that it can be approximated uniformly on compact intervals by step mappings with well-ordered steps.

(a) g has at most a countable number of discontinuities.

Moreover, there may be at most a countable number of spectral singularities on the continuous spectrum of the examined operators.

So Z must have at most a countable number of discontinuities, and then it must be left-continuous at each t except possibly on a dt-null set.

Since F is analytic in C + and is a 4π periodic function, we find that S 1 has at most a countable number of elements.

Under the condition (3.5), we have: (i) The set of eigenvalues of L is bounded, has at most a countable number of elements, and its limit points can lie only in a bounded subinterval of the real axis.

In all of these studies, the examined operators have a pure continuous spectrum, and the continuous spectrum consists of a half-line or union of lines pass from origin; moreover, there may be at most a countable number of spectral singularities on the continuous spectrum of the examined operators.

Two atoms E 1 and E 2 are said to be non-equivalent if d ( E 1, E 2 ) = μ ( E 1 Δ E 2 ) > 0. In this case μ ( E 1 ∩ E 2 ) = 0. Any σ-finite measure has at most a countable number of pairwise non-equivalent atoms (e.g. [[30], p.55]).

In general, nothing need be assumed about this set; in what follows, I will assume that E is at most countable, that is, that there are at most countably many evidence items.

Though only one field has been considered thus far, the formalism is easily generalizable to a countable number of fields with an associated set of countably indexed field operators φk(x) — cf. (Streater and Wightman 1964).

Only a countable number of attempts have been made in this regard.