Suppose that {f n } is a sequence of real-valued functions on &reals;. Suppose it converges to a continuous function f uniformly on each closed and bounded subset of &reals;. Which of the following statements is always true?

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Mathematics · Real Analysis

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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The sequence {f n } converges to f pointwise on &reals;

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Answer 1

For all sufficiently large n, the function f n is continuous

Answer 2

For all sufficiently large n, the function f n is bounded

Answer 3

The sequence {f n } converges to f pointwise on &reals;

Answer 4

The sequence {f n } converges to f uniformly on &reals;

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