<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>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [measure-theory]

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

      0
      votes
      0answers
      66 views

      Duality mapping of a the space of continuous functions? [on hold]

      The duality map $J$ from a Banach space $Y$ to its dual $Y^{*}$ is the multi-valued operator defined by: $J(y)=\{\phi\in Y^{*}:\, \left< y,\phi\right >=\Vert y\Vert^{2}=\Vert \phi \Vert^{2}\},...
      10
      votes
      1answer
      338 views
      +50

      A question concerning Lusin’s Theorem

      We consider only the set $M$ of a.e. essentially locally bounded measurable functions $[0, 1] \to \mathbb R$. Here $m(S)$ denotes the Lebesgue measure of $S$. Let $f$ be measurable. For every $e$ in $...
      3
      votes
      1answer
      119 views

      Volume form under holomorphic automorphisms

      $(M,\omega)$ is a compact Kaehler manifold and $f_{t,s}$ are 1-parameter group generated by holomorphic vector fields $V_s$. My question is whether the function $\frac{f_{t,s}^* \omega^n}{\omega^n}$ ...
      3
      votes
      1answer
      94 views

      If the finitely additive measure of an open set is approximable by clopen sets, is it approximable from within?

      Let $F$ be a finite set equipped the discrete topology. Let $X = F \times F \times ...$ be the countably infinite product space equipped with the product topology. Let $\mathcal A$ be any field of ...
      3
      votes
      1answer
      104 views

      Equivalent notion of approximate differentiability

      Is it true that the definition of approximate differentiability presented here of a function $f: \mathbb{R}^N \to \mathbb{R}$ is equivalent to the following one? $$\lim_{r \to 0} \rlap{-}\!\!\int_{...
      0
      votes
      1answer
      99 views

      Finitely additive measure on Cartesian square of countable set

      Let $\mu$ be a probability measure on $(\omega, 2^\omega, \mu)$ measure space which is finitely additive and $\mu(A)=0$ for finite sets. We can define as usual $\mu^2$ on semiring $\mathcal{G}=\{A\...
      1
      vote
      0answers
      33 views

      Formal justification of the Chaos game in the Sierpinsky triangle

      I want to justify why the Chaos game works to produce Sierpinsky triangle. I use a theorem taken from Massopoust Interpolation and Approximation with Splines and Fractals. Suppose that $(X,d)$ is a ...
      4
      votes
      2answers
      121 views

      Box dimension of the graph of an increasing function

      This Hausdorff dimension of the graph of an increasing function shows that: Let $f$ be a continuous, strictly increasing function from $[0,1]$ to itself with $f(0)=0, f(1)=1$. Then $dim_H \; G = ...
      3
      votes
      0answers
      59 views

      Functional characterization of local correlation matrices?

      Definition: A matrix $C\in\mathbb R^{m\times n}$ is local correlation matrix iff there exists real random variables $x_1,\dots,x_m,y_1,\dots,y_n$ defined on a common probability space which takes ...
      3
      votes
      0answers
      131 views

      Largest weak(-like) topology with respect to which continuous functions are dense in the space of Borel functions

      Let $X$ denote the space of bounded Borel functions $f\colon [0,1] \to \mathbb{R}$. Let $M$ denote the space of finite Borel measures on $[0,1]$. What is the largest family $F \subset M$ such that for ...
      6
      votes
      1answer
      186 views

      Compactness of set of indicator functions

      Let $\chi_A(x)$ denote an indicator function on $A\subset [0,1]$. Consider the set $$K=\{\chi_A(x): \text{ A is Lebesgue measurable in }[0,1]\}.$$ Is this set compact in $L^\infty(0,1)$ with respect ...
      3
      votes
      0answers
      64 views

      Is there a T3½ category analogue of the density topology?

      Motivation: I understand that various attempts have been made at defining a topology on $\mathbb{R}$ that is an analogue of the density topology?([1]) but for category (and meager sets) instead of ...
      2
      votes
      1answer
      182 views

      Can the characteristic function of a Borel set be approached by a sequence of continuous function through a certain convergence in $L^\infty$?

      Want to find $f_n$ a sequence of continuous functions, so that for all Borel regular measure $\mu$, we have $\int f_n d\mu\rightarrow\int \chi_\Delta d\mu$, as $n$ goes to infinity, where $\Delta$ ...
      1
      vote
      1answer
      99 views

      Measurable function

      Let $S$ be a countable set. Consider $X=S^{\mathbb{N}\cup\{0\}}$ the topological Markov shift equipped with the topology generated by the collection of cylinders. Denoted $\mathcal{B}$ as the Borel $\...
      -1
      votes
      0answers
      44 views

      Identical push-forward but not stationary

      I'm having some trouble coming up with a counter-example for this problem: Give an example of a stochastic process $\{X_n : n \in \mathbb{Z}^+\}$ on $(\Omega, \mathcal{F}, P)$ such that $P_{X_n} = P_{...

      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>