Abstract
The various notions of stability usually associated with dynamic systems are cast as uniform continuities. The features of Liapunov functions which typify stability are generalized to a characterization of uniform continuity. General theorems yield necessary and sufficient Liapunov criteria for weak and asymptotic stability and for uniform convergence of series and integrals. For the latter a common generalization of theorems of Weierstrass, Abel and Dirichlet is derived.
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