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Unless I misunderstand the question these seem to be complementing events with probabilities $p$ and $1-p$.

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Since the authors state that the total labor input is: $$\int t_i(k)dk$$ the meaning of the total labor input in this case would be that it is the sum of all attention $t_i$ allocated over those tasks $k$. For example if we would assume that $t_i (k) = k$ then the labor supply across continuum given by $[0,1]$ would be equal to $\frac{1}{2}$ because \$\int k ...

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Take a look at 120 years of higher education. Table 25 (in my edition) has state enrollments going back to 1869.

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The Industrial Revolution was an important watershed in women’s work in that it shifted the location of work out of the home. Because of the importance of machines powered by water wheels or steam engines, textiles began to be produced in factories rather than in workers’ homes. This change in the location of work made it more difficult for women to combine ...

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