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If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

how to show strictly increasing function on an interval has continuous inverse [duplicate]

If $f\in \mathcal{R}[a,b]$ satisfies $\int_a^b |f(x)|dx=0$ then $f=0$ almost everywhere.

Characterizing discontinuous derivatives

Is the derivative of a differentiable Lipschitz function also Lipschitz?

Is $\limsup_n \frac{\sigma(n)}{n \log p(n)} <\infty$, where $p(n)$ is the greatest prime factor of $n$ and $\sigma(n)=\sum_{d | n} d$?

convergence of a subsequence of function for a given rational in a closed interval

Must a continuous and periodic functions have a smallest period?

Continuous extension of XOR

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

If $f:\mathbb R^2 \to \mathbb R$ continuous on straight lines and $f(\text{compact})= \text{compact}$, then $f$ continuous?

Can the idea of a 'function of a variable' be made rigorous?

ask a question about generalized Dominated Convergence Theorem

Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$

Showing a recursive sequence is Cauchy

Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$

Lipschitz Continuity of Linear Map Between Finite Dimensional Vector Spaces

For any bounded subset $E$ of the real line, if f is continuous over the entire real line, is $f(E)$ also bounded?

New posts in real-analysis

Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$

How does one determine which variables to do induction on?

If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

how to show strictly increasing function on an interval has continuous inverse [duplicate]

If $f\in \mathcal{R}[a,b]$ satisfies $\int_a^b |f(x)|dx=0$ then $f=0$ almost everywhere.

Characterizing discontinuous derivatives

Is the derivative of a differentiable Lipschitz function also Lipschitz?

Is $\limsup_n \frac{\sigma(n)}{n \log p(n)} <\infty$, where $p(n)$ is the greatest prime factor of $n$ and $\sigma(n)=\sum_{d | n} d$?

convergence of a subsequence of function for a given rational in a closed interval

Must a continuous and periodic functions have a smallest period?

Continuous extension of XOR

Is there a closed form for $\int_a^b\frac{{\rm arccosh}x}{\sqrt{(x-a)(b-x)}}$?

If $f:\mathbb R^2 \to \mathbb R$ continuous on straight lines and $f(\text{compact})= \text{compact}$, then $f$ continuous?

Can the idea of a 'function of a variable' be made rigorous?

ask a question about generalized Dominated Convergence Theorem

Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$

Showing a recursive sequence is Cauchy

Positive integers $k = p_{1}^{r_{1}} \cdots p_{n}^{r_{n}} > 1$ satisfying $\sum_{i = 1}^{n} p_{i}^{-r_{i}} < 1$

Lipschitz Continuity of Linear Map Between Finite Dimensional Vector Spaces

For any bounded subset $E$ of the real line, if f is continuous over the entire real line, is $f(E)$ also bounded?