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TIFR Mathematics 2022 | Part B | Question-15

Answer whether the following statements are True or False.

There exists $f \in C([0,1], \mathbb{R})$ satisfying the following two conditions:

  1. $\int_{0}^{1} f(x) d x=1$; and
  2. $\lim _{n \rightarrow \infty} \int_{0}^{1} f(x)^{n} d x=0$.
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