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 Oct31 comment Let $L_p$ be the complete, separable space with $p>0$. This is very inaccurate. b) is asked on this question. Oct28 revised Borel $\sigma$ algebra on a topological subspace. edited body Oct26 revised system of open intervals added 3 characters in body Oct26 revised Linear Independent Rows vs. Columns added 1 characters in body Oct25 revised A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous edited title Oct25 revised The bonus question in calc class. TeX Oct15 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 Oct15 revised Determining a set is closed spelling Oct15 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. Oct15 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 $X$ Oct15 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.. Oct15 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. Oct15 revised How to prove that $f(x)$ is discontinuous at infinitely many points on $(0,1)$? Improved formatting and some minor typos. Oct15 revised Derivating $f(t)=\int_0^t x dx$ using measure theory changing \sim by \setminus. Oct10 comment Cantor set and countability. The set of endpoints of these countably many intervals is strictly contained in the Cantor set. The Cantor set is perfect and therefore uncountable. Oct10 answered Linear Independent Rows vs. Columns Oct10 revised Linear Independent Rows vs. Columns TeX Oct10 revised $f(x)=0$ implies $f(g(y))=0$ for some $y$? edited title Oct8 comment Absolute value of Lebesgue integrable function Look at $f^+$ and $f^-$ Oct8 comment Riemann-Lebesgue Integrable @Potato Why it suffices? There are non Riemann integrable functions which are equal a.e. to a Riemann integrable function