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Is every topological space is measurable?
Actually I am learning about measure theory. But I have confusion between topological space and measurable . Is there any relationship among them or not?
Apr 18, 2026
Archive: News
news
Given mu and sigma of a normal distribution, how to find min and max?
I am trying to calculate the min and max values for Gaussian noise where mu=0 and sigma=0.02. It looks like it is 0.08 and -0.08 from the picture from htt...
Apr 18, 2026
news
How to check if the integral of a function is correct with a scientific calculator?
As a calculus student I would like to know if there is any way to verify the "correctness" of an integral of a function using a calculator. I mean if have...
Apr 18, 2026
news
Is "ln" (natural log) and "log" the same thing if used in this answer?
Find $x$ for $4^{x-4} = 7$. Answer I got, using log, was ${\log(7)\over 2\log(2)} + 4$ but the actual answer was ${\ln(7)\over2\ln(2)} + 4$ I plugged both...
Apr 18, 2026
news
How quickly can you mess up a domino tiling in 3D?
Suppose that we are trying to tile $\mathbb{Z}^3$ with dominoes, i.e., two face-adjacent cubes. We start going about this haphazardly, laying dominoes in ...
Apr 18, 2026
news
Prove that $K_{3,3}$ is not planar.
Prove that $K_{3,3}$ is not planar. This problem comes from A Course in Combinatorics (Problem 1D). At this point, the authors have introduced merely the ...
Apr 18, 2026
news
Correlation Coefficient and Determination Coefficient
I'm new to linear regression and am trying to teach myself. In my textbook there's a problem that asks "why is $R^{2}$ in the regression of $Y$ ...
Apr 18, 2026
news
Deck transformations of universal cover are isomorphic to the fundamental group - explicitly
I have read on several places that given a (say path connected) topological space $X$ and its universal covering $\tilde{X}\stackrel{p}\rightarrow X$, the...
Apr 18, 2026
news
Prove that if $f$ is continuous and $f$ is equal to its integral from 0 to $x$, then $f(x) = 0$ for all $x$
The question is basically we have a continuous function $f:R\to R$ in which we have $$f(x)=\int_0^xf$$ for all real x, and it asks us to show that $f(x) =...
Apr 18, 2026
news
Domain of Moment Generating Function Bernoulli
I want to find the domain of a Moment Generating Function of random variable k following a Bernoulli distribution. This means that: \begin{equation} f(k;p...
Apr 18, 2026
