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Oct
31
revised Does $\chi_{[n,n+1]}\to 0$ almost everywhere?
Improving title
Oct
31
revised Convergence a.e. and of norms implies that in Lebesgue space
added 4 characters in body; edited title
Oct
31
revised Convergence a.e. and of norms implies that in $L^1$ norm
Improving title
Oct
31
comment Sequence of continuous fuctions $f_n:[0,1]\rightarrow [0,1]$ s.t. $\lim_{n\rightarrow\infty}m(E_n(\varepsilon)) = 0$ but…
Doesn't this answer your question?
Oct
31
revised Does $\lim_{n\rightarrow \infty} \int_X f_n - \int_X f\gt 0$ implies that convergence of $f_n$ to $f$ a.e. fails?
Formmating
Oct
31
comment Can $\int|f_n|d\mu \to \int |f|d\mu$ but not $\int|f_n - f|d\mu \to 0$?
Exact dupe of this
Oct
31
comment Let $L_p$ be the complete, separable space with $p>0$.
This is very inaccurate. b) is asked on this question.
Oct
28
revised Borel $\sigma$ algebra on a topological subspace.
edited body
Oct
26
revised system of open intervals
added 3 characters in body
Oct
26
revised Linear Independent Rows vs. Columns
added 1 characters in body
Oct
25
revised A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
edited title
Oct
25
revised The bonus question in calc class.
TeX
Oct
15
revised Prove $\lim_{x\to p}(f+g)(x)=\lim_{x\to p}f(x)+\lim_{x\to p}g(x)$
added 1 characters in body; edited title
Oct
15
revised Determining a set is closed
spelling
Oct
15
comment How to prove that the sum of two compact sets in a Banach space need not be compact
You are asking if the sum of a compact set and a closed ball is compact in a Banach space. The closed balls need not be compact.
Oct
15
comment How to prove that the sum of two compact sets in a Banach space need not be compact
@kevin This says also how to construct a counter example: take $X$ a space where the closed unit ball is not compact and consider $K$ a compact subset of $X$
Oct
15
comment How to prove that the sum of two compact sets in a Banach space need not be compact
...and the closed unit ball is compact iff..
Oct
15
comment How to prove that $f(x)$ is discontinuous at infinitely many points on $(0,1)$?
I have edited your post, please let me know if this really agree with what you want to ask. Since you have already received at least one good answer to each you've asked please consider accept your answers.
Oct
15
revised How to prove that $f(x)$ is discontinuous at infinitely many points on $(0,1)$?
Improved formatting and some minor typos.
Oct
15
revised Derivating $f(t)=\int_0^t x dx$ using measure theory
changing `\sim` by `\setminus`.