Measure Theory — Topic Summaries
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Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2
Assigning a nonzero probability to every exact real value of an unknown parameter leads to a paradox: there are uncountably many candidate values, so...
Music And Measure Theory
A ratio of musical frequencies can sound harmonious or cacophonous depending less on whether it is rational or irrational, and more on how well it...
Measure Theory 9 | Fatou's Lemma [dark version]
Fatou’s Lemma gives a one-sided way to move “liminf” through an integral for non-negative measurable functions. Instead of asking whether an integral...
Measure Theory 16 | Proof of the Substitution Rule for Measure Spaces [dark version]
The substitution rule for measure spaces lets integrals be transferred across a measurable map: integrating a function on Y with respect to the image...