<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Questions tagged [measure-theory]

      Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

      Filter by
      Sorted by
      Tagged with
      0
      votes
      0answers
      17 views

      Canonical measure on Pareto front?

      Suppose $F:\mathbb R^d\to\mathbb R^D$ encodes a set of objective functions on $\mathbb R^d$, and take $\mathcal S\subseteq \mathbb R^D$ to be the Pareto front of $F$. Under some genericity/smoothness ...
      1
      vote
      1answer
      68 views

      Measure of real numbers with converging average over binary digits

      Consider the unit interval $[0,1]$, and by digits of $x\in[0,1]$ I mean its binary digits after the separator with no 1-period. If $x_1,x_2,x_3,...$ are the digits of $x$, then consider the $k$-th ...
      2
      votes
      1answer
      182 views

      How can the same polytope have three different volumes?

      I'm quite new to geometry and I came across the idea that the same convex polytope can have at least three different volumes. Consider the permutohedron, formed by the convex hull of the n! points ...
      0
      votes
      0answers
      21 views

      Predictable Projection of a Stopped Process (Typo in Jacod & Shiryaev?)

      Given a filtered probability space $( \Omega, \mathcal{F}, (\mathcal{F}_t)_t, \mathbb{P})$ and an $\mathcal{F} \otimes \mathcal{B}(\mathbb{R}_+)$-measurable bounded process $X: \Omega \times \mathbb{R}...
      3
      votes
      1answer
      141 views

      Must a locally compact, second countable, Hausdorff space support a Radon measure?

      Let $X$ be a locally compact, second countable and Hausdorff space, must there be a Radon measure on $X$ whose support is $X$? The motivation for this question comes from Anton Deitmar's paper On ...
      0
      votes
      0answers
      59 views

      Volume form induces Borel measure: proof verification [migrated]

      Disclaimer: I asked this question already on the regular mathematics site here, but to no avail, even with a bounty. I think answering said question is still of value. Proposition. Let $M$ be a ...
      1
      vote
      0answers
      73 views

      Probability space with countable subset such that every subset of positive measure meets the subset

      Let $(X, \mathcal F, P)$ be a probability space. Question What kind of condition is this: there exists a sequence $(a_n)_n \subseteq X$ such that $\forall$ measurable $A \subseteq X$, $P(A) >...
      3
      votes
      1answer
      136 views

      Is every closed subset of finite measure contained in an open subset of finite measure?

      Could someone will verify my statement: For every locally finite Borel measure on metric space and closed set $F$ with finite measure, there exists open set $U$ such that $F \subset U$ and $U$ has ...
      -1
      votes
      1answer
      47 views

      Existence of sequence of measurable sets with prescribed densities

      Consider Lebesgue measure $m$ on $[0, 1]$. Fix a countable sequence $a_i, 0 < a_i < 1$ such that $\sum_i a_i = 1$. Is there a sequence of disjoint measurable subsets of $[0, 1]$, $E_i$ whose ...
      0
      votes
      0answers
      32 views

      Is there a dyadic cube decomposition where edge length is comparable to L^2 averages?

      Suppose I have some measurable function $f : B_1(0) \to [0,1)$, which is pointwise very small, i.e. $\|f\|_{\infty} << 1$. I'm looking to construct some kind of dyadic cube decomposition or ...
      4
      votes
      1answer
      91 views

      Is there a density theorem for Banach measure?

      Fix a finitely additive measure $\mu$ on $\mathbb R^2$ that is consistent with the Lebesgue measure. Does Lebesgue's density theorem hold for such a $\mu$, i.e., is it true that for every $A$ we have $...
      1
      vote
      0answers
      57 views

      Regularity of locally finite Borel measure

      Do you know any proof that locally finite Borel measure on metric space is regular ? I found many proofs only for finite Borel measure, but it's not satisfies me. Or maybe do you know any books or ...
      3
      votes
      1answer
      196 views

      Attractors in random dynamics

      Let $\Delta$ be the interval $[-1,1]$, then we can consider the probability space $(\Delta , \mathcal{B}(\Delta),\nu)$, where $\mathcal{B}(\Delta)$ is the Borel $\sigma$-algebra and $\nu$ is equal ...
      -1
      votes
      0answers
      46 views

      Union of 2-dilation of a Lebesgue measurable set is real line R?

      Def : Frame Wavelet Set Let $E$ be a Lebesgue measurable set of finite measure. Define $\psi \in L^{2}(R)$ by $\hat{\psi}=\frac{1}{\sqrt{2\pi}} \chi_{E}$, where $\hat{\psi}$ is Fourier Transform of $\...
      1
      vote
      0answers
      31 views

      What is the Wiener measure of the set of curves with given Hölder constant on a Riemannian manifold?

      Let $M$ be a connected Riemannian manifold and $x_0 \in M$. For $0 < \alpha < \frac 1 2$, let $$H = \{ c : [0,1] \to M \mid c(0) = x_0 \text{ and } \exists C>0 \text { s.t. } d(c(s), c(t)) \...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>

              解太湖3d字谜解释 辽宁十一选五开奖号码 极速赛车彩票计算方法 福安徽时时 重庆时时彩五分彩开奖记录 极速时时选号怎么选的 北京赛pk10官网开奖 今晚31选7开奖结果 最准确双色球预测号码彩经网 网络捕鱼怎么控制玩家