[分析] Change order of limit

[chopriabin ()]

Suppose that

1. f(x) is a continuous nonnegative function for x in R with the property that f(x) is non-increasing in x and \int_{0}^{\infty} f(x) dx<\infinity.


2. {x_n} is a nonnegative sequence with x_n converging to x_0 when n tends to infinity.


Must f(x_n) approach to f(x_0) as x_n tends to infinity ? Prove or disprove.


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