Constructing examples
Problem1. Help me. Construct a sequence of continuous functions $\Phi_n$
satisfying the conditions 1. supp $\Phi_n \subset (1, n)$. 2. $0 \leq
\Phi_n \leq 1$. 3. $\lim\limits_{n \to \infty}\int_1^n
\dfrac{\Phi_n(\tau)}{\tau}d\tau = \infty$.
Problem 2. Construct a sequence $f_n(t)$ of bounded functions on $[0,1]$
converging to zero in $L^1$ so that $f_n$ converges at no point in
$[0,1]$.
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