### Questions (25)

 9 A formula for $\lfloor n\rfloor+\left\lfloor \frac n2\right\rfloor+ \left\lfloor \frac n3\right\rfloor+\ldots+\left\lfloor \frac nk\right\rfloor$? 5 calculate $\prod_1^\infty k^{\frac1{k!}}$ 4 Convergence of $\sum\frac{a_n}{b_n}$ and $\sum (\frac{a_n}{b_n})^2$ implies convergence of $\sum\frac{a_n}{a_n+b_n}$ [duplicate] 3 If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$. 3 Show that $\mu_n=\frac1n\sum_1^n\epsilon(j)$ has infinitely many weak$^*$ limit point

### Reputation (649)

 +5 A formula for $\lfloor n\rfloor+\left\lfloor \frac n2\right\rfloor+ \left\lfloor \frac n3\right\rfloor+\ldots+\left\lfloor \frac nk\right\rfloor$? +5 Convergence of a sequence of subspaces +5 Relation between weak * topology of $X^*$ and relative norm topology +5 reference request: $K$ is relatively weakly compact in $C(X)$ iff $K$ is relatively pointwise compact in $C(X)$

 9 Is it true that $\partial\partial E=\partial E$ 2 Riemann-Stieltjes integrablity 1 Is there an inequality that $\|a+b\|^2 \le \|a\|^2 + \|b\|^2$? 1 Show that the function is measurable 1 Showing that Each Member of the Cantor Set has a Unique Representation as a Particular Series

### Tags (43)

 15 real-analysis × 25 1 measure-theory × 3 2 analysis × 10 1 metric-spaces × 3 2 riemann-integration 1 norm 1 functional-analysis × 12 1 continuity 1 normed-spaces × 6 1 complex-numbers