Extended real numbers $\mathbb{R}^*$ are real numbers with 2 additional elements $+\infty$ and $-\infty$ that obey certain properties of inequalities. Operations are not defined on extended real ...
analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
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constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
A Cauchy real number is a real number that is given as…
I am currently self-studying Measure, Integration & Real Analysis by Axler, and I am struggling to understand the motivation behind the definition of a measurable function.
The definition I am ...
