Is the following true? For any linear functional $A$ from $L_1(S,\Sigma,\mu)\to\mathbb{R}$ there is a sequence of continuous linear functionals $\{B_k\}_{k=1}^\infty$ so that for all $f\in L_1(S,\Sigma,\mu)$ , $\lim_{k\to\infty} B_k[f]=A[f]$. Might it help if $\mu$ is a probability measure?
2026-05-15 09:42:34.1778838154
Is every linear functional of L1 the pointwise limit of a sequence of continuous linear functionals?
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