An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue quadratures (for $f$ and $g$) from two eigenproblems, the projections of $f$- and $g$- eigenvectors on each other allow to build a joint distribution estimator, the most general form of which is a density-matrix correlation. Examples of the density-matrix correlation can be a value-correlation $V_{f^{[i]};g^{[j]}}$, similar to a regular correlation concept, and a new one, a probability-correlation $P_{f^{[i]};g^{[j]}}$. If Christoffel function average is used instead of regular average the approach can be extended to an estimation of joint probability of three and more random processes. The theory is implemented numerically; the software is available under the GPLv3 license.

翻译：开发了Lebesgue Inducture arxiv:1807.06007的重要应用。 在两个随机过程(f(x)美元和g(x)美元)的情况下,可以制定和解决两个通用的egenval 问题。除了从两个基因问题中获取两个Lebesgue eqrature(f美元和g美元)外,还从两个基因问题中获取两个Lebesgue eqrature(f美元和g美元),预测的美元-和g-egenevors aniv:1807.0607,07美元,其中最一般的形式是密度-矩阵关系。密度-矩阵关系的例子可以是价值-orlation $V ⁇ f ⁇ [i];g{{j} $(j)$) $(j) 和 eg- eg- genevorlation $(i) ;g} {_}。如果使用Christoffel 平均函数,而不是正常的平均值,那么 方法可以扩展为三种或更随机程序的联合概率估计。理论是用数字式的。根据GPL3提供的。