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essential supremeessential supremeAs is often the case in measure-theoretic questions, the definition of essential supremum and infimum does not start by asking what a function $${\displaystyle f}$$ does . See more
essential supreme• $${\displaystyle L^{p}}$$ space – Function spaces generalizing finite-dimensional p norm spaces See moreOn the real line consider the Lebesgue measure and its corresponding 𝜎-algebra $${\displaystyle \Sigma .}$$ Define a function $${\displaystyle f}$$ by the formulaThe supremum of this function (largest value) is 5, and the . See more1. ^ For nonmeasurable functions the definition has to be modified by assuming that $${\displaystyle f^{-1}(a,\infty )}$$ is contained in a set of measure zero. Alternatively, one can assume that the measure is complete.1. See more
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