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Bayesian philosophers see the conditional relationship as more basic than that of joint events - that is, more compatible with the organization of human knowledge. In this view, B serves as a pointer to a context or frame of knowledge, and A I B stands for an event A in the context specified by B (e.g. , a symptom A in the context of a disease B).Consequently, empirical knowledge invariably will be encoded in conditional probability statements, whereas belief in joint events (if it is ever needed) will be computed from those statements via the product peA, B) = peA I B) P(B), (1.9) which is equivalent to (1.8).
Judea Pearl - Causality_ Models, Reasoning, and Inference-Cambridge University Press
2000
Genes are the primary policy-makers; brains are the executives. But as brains became more highly developed, they took over more and more of the actual policy decisions, using tricks like learning and simulation in doing so. The logical conclusion to this trend, not yet reached in any species, would be for the genes to give the survival machine a single overall policy instruction: do whatever you think best to keep us alive.
The Selfish Gene
Richard Dawkins
The main difference between integrability in the sense of Lebesgue and Riemann is the way we measure 'the area under the curve'. The Riemann integral asks the question what's the 'height' of 𝑓f above a given part of the domain of the function. The Lebesgue integral on the other hand asks, for a given part of the range of 𝑓f, what's the measure of the 𝑥x's which contribute to this 'height'.
Integration - ELI5: Riemann-Integrable vs Lebesgue-Integrable - Mathematics Stack Exchange
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