query: Integration of the Sequence $\cos^2(nx+u_n)$ over a Measurable Set.
positive_passages.docid: 142249
positive_passages.text: Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$
negative_passages.docid: 53363
negative_passages.text: Ultralimit of an eventually constant generalized sequence
negative_passages.docid: 37906
negative_passages.text: Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
negative_passages.docid: 122585
negative_passages.text: Show that a function almost everywhere continuous is measurable
negative_passages.docid: 114947
negative_passages.text: Bounded variation implies Borel measurable
negative_passages.docid: 153121
negative_passages.text: show that $\{x_n\}$ is a cauchy sequence
negative_passages.docid: 61199
negative_passages.text: Integration by parts for general measure?
negative_passages.docid: 47923
negative_passages.text: For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$
negative_passages.docid: 83825
negative_passages.text: $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$
negative_passages.docid: 97841
negative_passages.text: General property regarding outer measure for a nested sequence of sets (measurable or not).
negative_passages.docid: 148759
negative_passages.text: The Radon-Nikodym derivative of a measure such that $|\int f'\,d\mu|\le \|f\|_{L^2}$ for $f\in C^1$
negative_passages.docid: 87338
negative_passages.text: Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$
negative_passages.docid: 1474
negative_passages.text: How to prove limit of measurable functions is measurable
negative_passages.docid: 32347
negative_passages.text: Limit of a decreasing sequence of measurable sets.
negative_passages.docid: 60988
negative_passages.text: Convergence in measure - product
negative_passages.docid: 125910
negative_passages.text: Continuity of Integration for a measurable function
negative_passages.docid: 132448
negative_passages.text: Prove that: $\int_0^{n\pi}f(\cos^2(x))\,dx=n\int_0^{\pi}f(\cos^2(x))\,dx?$