Let f be a function from R~p to R~q and let A be a finite set of pairs (θ, η) ∈ R~p x R~q. Assume that the real-valued function {η, f(x)) is Lipschitz continuous in the direction θ for every (θ, η) ∈ Λ. Necessary and sufficient conditions on A are given for this assumption to imply each of the following: (1) that f is Lipschitz continuous, and (2) that f is continuous with modulus of continuity ≤ Cε|log_ε|.
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机译：设f是从R〜p到R〜q的函数，并且让A是对（θ，η）∈R〜p x R〜q的有限对。假设对于每个（θ，η）∈Λ，实值函数{η，f（x））在方向上都是Lipschitz连续的。为此假设提供了关于A的充要条件，以暗示以下各项：（1）f是Lipschitz连续的，和（2）f以连续模数≤Cε|log_ε|连续。
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