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Every uniformly convergent sequence of bounded function is uniformly bounded? - Answers

The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|



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Every uniformly convergent sequence of bounded function is uniformly bounded? - Answers

https://math.answers.com/math-and-arithmetic/Every_uniformly_convergent_sequence_of_bounded_function_is_uniformly_bounded

The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|



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https://math.answers.com/math-and-arithmetic/Every_uniformly_convergent_sequence_of_bounded_function_is_uniformly_bounded

Every uniformly convergent sequence of bounded function is uniformly bounded? - Answers

The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|

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