论文标题
敏感的随机变量在每一个$ l^{p}（\ Mathbb {r}，\ Mathscr {b} _ {\ Mathbb {r}}，\ Mathbb {p}）$中的敏感随机变量密集
Sensitive Random Variables are Dense in Every $L^{p}(\mathbb{R}, \mathscr{B}_{\mathbb{R}}, \mathbb{P})$
论文作者
论文摘要
我们表明，对于每$ 1 \ leq p < +\ infty $，并且对于每一个borel概率度量$ \ mathbb {p} $，$ \ mathbb {r} $，$ l^{p}的每个元素（\ mathbbbb {r} $ l^{p} $ - 某些有界随机变量序列的限制，这些变量几乎是lebesgue，几乎可以差异化，而衍生物的范数在每个可分割性的每个点都具有大于任何预先指定的实际数字。通常，此结果为$ \ Mathbb {r} $上的$ l^{p} $ functions提供了$ l^{p} $ - 近似的更精细描述。
We show that, for every $1 \leq p < +\infty$ and for every Borel probability measure $\mathbb{P}$ over $\mathbb{R}$, every element of $L^{p}(\mathbb{R}, \mathscr{B}_{\mathbb{R}}, \mathbb{P})$ is the $L^{p}$-limit of some sequence of bounded random variables that are Lebesgue-almost everywhere differentiable with derivatives having norm greater than any pre-specified real number at every point of differentiability. In general, this result provides, in some direction, a finer description of an $L^{p}$-approximation for $L^{p}$ functions on $\mathbb{R}$.
