If this sequence is uniformly bounded and equicontinuous, then there exists a subsequence ('f'n'k') that uniform convergence.

The first, and simpler, version of the theorem states that a uniformly bounded family of holomorphic functions defined on an open subset of the complex numbers is normal.

The assumption that U C implies that these radii are uniformly bounded.

Then the norm of h is less than that of g. Thus these norms are uniformly bounded.

If this sequence is uniformly bounded and equicontinuous, then there exists a subsequence (ƒ'n) that converges uniformly.

In 1964, Golod and Shafarevich constructed an infinite group of Burnside type without assuming that all elements have uniformly bounded order.

Since H is a bounded operator, it follows that the operators H are uniformly bounded in operator norm on L(T).

The L norms of these functions are uniformly bounded.

In a model with more than one time then the wealth process associated with an admissible trading strategy must be uniformly bounded from below.

The family of derivatives of the above family, is not uniformly bounded.