Expectation arises as linear averaging in probability coordinates defined by the CDF, pulled back to value space, coinciding with Kolmogorov means and extending to heavy-tailed cases via boundary concentration.
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Probability Geometry and Kolmogorov Expectations via Coordinate Charts
Expectation arises as linear averaging in probability coordinates defined by the CDF, pulled back to value space, coinciding with Kolmogorov means and extending to heavy-tailed cases via boundary concentration.