There is a rich body of literature on equalities in the period life table, which also can be interpreted as a stationary population, and a smaller, but no less rich, body on inequalities. The latter is important because it provides information on health disparities and, like the equality literature, serves as a foundation for formal mortality analysis. We straddle both of these bodies by reconciling a known inequality such that a new mathematical equality emerges in the period life table. We then show that this new equality links life expectancy at birth (mean age at death) directly to the average lifespan of the living members of a stationary population. This linkage represents a second newly identified equality in this paper that has the potential to yield useful insights because it links the average lifespan of the living members of a stationary population directly to elements that are central to the dynamics and structure of a stationary population, life expectancy, and variance in age at death.

在生命周期表中有大量关于平等的文献，也可以解释为固定的人口，以及关于不平等的较小但同样丰富的文献。后者很重要，因为它提供了有关健康差异的信息，并且与平等文献一样，可以作为正式死亡率分析的基础。我们通过调和已知的不等式来跨越这两个实体，以便在周期生命表中出现新的数学等式。然后，我们表明，这种新的平等将出生时的预期寿命（平均死亡年龄）与固定人口中活着的成员的平均寿命直接联系起来。