# Questions tagged [analysis]

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

43,404 questions
Filter by
Sorted by
Tagged with
1 vote
7 views

• 796
46 views

### Alternate proof to the Extreme Value Theorem

I'm following Spivak's Calculus and was revisiting some of my notes when I think I found a much more straightforward proof for the Extreme Value Theorem, compared to the one given in the book. I was ...
• 281
1 vote
38 views

### Composition of functions, once for all

I need certainties. Consider two functions $f: A \to B$ and $g: C \to D$. For what I am going to ask, it's not a loss of generality if we consider multivariable functions with domains and or codomains ...
• 65
122 views

### What is this notion of continuity? Pt. 2

Let $f : \mathbb{Z}_p\to \mathbb{Z}_q$, where $\mathbb{Z}_p$ ($\mathbb{Z}_q$) are the $p$-adics ($q$-adics) for $p\neq q$. I have encountered the class of all $f$ satisfying \tag{1}\...
• 7,058
30 views

### If $(X, A, m)$ is $\sigma$-finite and $B\subseteq A$ is a $\sigma$-sub-algebra, then is $(X, B, \nu)$ $\sigma$-finite?

Here $\nu$ is defined in the following way: $$\nu(E)= \int_E f dm$$ where $f$ is non-negative, $A$-measureable. I don't see why we can assert that $\nu$ is also $\sigma$-finite since the subsets of $B$...
37 views

• 43
### Solving $f(x) = f(\frac{a + b x}{c + d x}) = f(\frac{a' + b' x}{c' + d' x})$?
How to solve the equation $$f(x) = f(\frac{a x + b}{c x + d}) = f(\frac{a'x + b'}{c'x + d'})$$ For given real $a,a',b,b',c,c',d,d'$ ? Maybe this system of equations is a bit overdetermined in its ...