- #1
MathematicalPhysicist
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I would like to know if there's a counterpart to the single variable theorem, that if f is a differentialble function with a bounded derivative, is uniformly continuous.
I think the counterpart should be, if f(x1,...,xn) is continuous function, and differentiable, and each f'_xi are bounded then f is uniformly continuous.
But I have my suspicions.
Anyone can corroborate or disprove this?
I think the counterpart should be, if f(x1,...,xn) is continuous function, and differentiable, and each f'_xi are bounded then f is uniformly continuous.
But I have my suspicions.
Anyone can corroborate or disprove this?