Sentence examples for be defined by for from inspiring English sources

Let be defined by for each.

Let the identity map and be defined by for.

Let,, and be defined by, for Then both and are u.s.c.s.c

Choose to be defined by for every and is defined by, where, with, for some,, and is defined by (2.17).

Choose to be defined by for every and is defined by, where,, and is defined by (2.35).

Let, and let be defined by for Then is an u.s.c. and convex set-valued map with convex compact values, and for each, and,.

Here is defined by for ; and for.

Note that and are defined by for.

Assume that is defined by, for, (323).

Here, is defined by for any.

where is defined by for all.