# Questions tagged [real-analysis]

Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

2,472 questions
33 views

97 views
+100

### How do we introduce a signed finite measure on the space of curves confined into the box $[0,1]^{n}$?

Given $\Omega_{n} = \{\alpha:[0,1]\rightarrow[0,1]^{n}\,|\,\alpha\,\,\text{is smooth}\}$, consider the equivalence relation: \begin{align*} & \alpha_{1} \sim \alpha_{2} \Leftrightarrow \int_{0}^{1}...
64 views

822 views

### Differentiating an integral that grows like log asymptotically

Suppose I have a continuous function $f(x)$ that is non-increasing and always stays between $0$ and $1$, and it is known that $$\int_0^t f(x) dx = \log t + o(\log t), \qquad t \to \infty.$$ ...
18 views

### Parametric statistics: how to estimate the supremum of a set of parameters from a random sample

I would like to ask a question on how to estimate the supremum norm of a set of parameters in the following setting. I appreciate any pointer or suggestion. Thanks. Question: Suppose we have $m$ ...
43 views

319 views

### How to compute this series: $\sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$ [closed]

How to compute this series: $$\sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$$ where $C_k$ is the catalan number: $C_k=\frac{1}{k+1}{2k \choose k}$. (Further, is there any general method to treat this ...