A probability measure is more like a cumulative distribution function. It gives, for any set of values, the probability of the random variable being in that set.

Jul 27, 2023 · A measure now assigns numbers to each event, which we can, for example interpret as probability or volume or something else. Therefore, it's reasonable to define …

Nov 25, 2024 · 0 Since we can not measure all sets (e.g. vitali sets), it makes sense that measures need to be defined on a reduced set of sets. This reduced set of sets is the set of …

Feb 24, 2013 · The measure of the discontinuities is actually a measure of the discontinuity of the function, and when it is zero, it another way of showing that f is continuous and hence …

Feb 9, 2022 · Is this the right way to construct the canonical measure on the Borel $\sigma$ -algebra of an oriented Riemannian manifold? If so, is this the most commonly used measure …

Thanks, but I am not even sure of how to define a measure on a single given chart, because I don't even know how a measure on a manifold nor on a given chart are defined.

Apr 10, 2025 · If you define a measure on the rational numbers (Donald Hobson's answer suggests two) and choose an enumeration of the rationals, then work through the construction, …

To truly have any understanding of a measure zero set, you need to understand this definition and the crucial examples that come immediately afterwards. First, note any countable (and hence …

Feb 22, 2024 · I have studied some basic measure theory, mainly from Rudin's Real and Complex Analysis and Cohn's Measure Theory, but I have not understood how to define Lebesgue …

How can I define a measure of similarity between two line segments in $\mathbb {R}^2$? Ask Question Asked 11 years, 6 months ago Modified 3 years, 10 months ago