Jun 11, 2025 · 6 "Every metric is continuous" means that a metric $d$ on a space $X$ is a continuous function in the topology on the product $X \times X$ determined by $d$.

Jan 21, 2024 · 1. What do you mean by weak topology on $ (0,T)$? 2. Yes, you have to distinguish between weakly continuous and weakly sequentially continuous maps.

Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest …

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

Intuitively, a continuous function is allowed to misbehave at the endpoints of an open interval (because it doesn't have to be defined at the endpoints), but it must behave itself on a closed …

Functions in this space are technically only defined up to equality "almost everywhere", so you can change the values of a continuous U function on $ [-1,1]$ arbitrarily on a set of measure …

1 Addition, subtraction, and multiplication are always continuous, on the reals, complexes and many other domains. Division is also continuous, as long as the denominator does not vanish. …

Apr 30, 2024 · Is every $\alpha$-Hölder continuous function of bounded variation absolutely continuous? Ask Question Asked 1 year, 6 months ago Modified 1 year, 6 months ago

The containment "continuous"$\subset$"integrable" depends on the domain of integration: It is true if the domain is closed and bounded (a closed interval), false for open intervals, and for …

Dec 28, 2015 · Typically the range of a continuous random variable is $\mathbb {R}$, $ [0,\infty)$, or some interval $ [a,b]$. Examples of continuous random distributions are the normal …