lebesgue measure related issues & queries in MathXchanger

Find, with a justification, the probability of E.

probability measure-theory
Updated October 21, 2018 14:20 PM

Show that $\alpha f + \beta g$ is measurable when $f,g$ are measurable.

measure-theory lebesgue-integral measurable-functions
Updated October 21, 2018 11:20 AM

About an inequality in Royden's Real Analysis

measure-theory inequality
Updated October 21, 2018 11:20 AM

Find m(A), where m denotes Lebesgue measure

measure-theory lebesgue-measure
Updated October 21, 2018 10:20 AM

Sufficient and neccesary condition for almost convergence of $\max (X_1,X_2,\cdots,X_n)/a_n$

probability-theory measure-theory
Updated October 21, 2018 10:20 AM

Power set in measure theory

measure-theory
Updated October 21, 2018 09:20 AM

Riemann Sums of Improper Integrals on Unbounded Domain

real-analysis analysis measure-theory
Updated October 21, 2018 08:20 AM

Finding possible p's for signed measure

measure-theory signed-measures
Updated October 21, 2018 08:20 AM

Lebesgue measure of intersection of sets

analysis measure-theory lebesgue-measure geometric-measure-theory
Updated October 21, 2018 07:20 AM

integration over general measure space (proposition 9, chapter 18.2 in Royden)

measure-theory
Updated October 21, 2018 01:20 AM

Understanding the integral of a sequence of functions

real-analysis limits lebesgue-integral sequence-of-function
Updated October 20, 2018 21:20 PM

understanding an estimation of the perimeter of sets, $|P(\hat{V})-P(V)|\le P(B_r(x))$

integration analysis measure-theory lebesgue-measure geometric-measure-theory
Updated October 20, 2018 19:20 PM

Examples about bounded variation function.

measure-theory lebesgue-integral lebesgue-measure examples-counterexamples bounded-variation
Updated October 20, 2018 17:20 PM

What is the expectation of $X$ given $X$

probability probability-theory measure-theory conditional-expectation
Updated October 20, 2018 16:20 PM

Construction of an Open, Dense, Connected Set in the Plane

real-analysis measure-theory lebesgue-measure
Updated October 20, 2018 15:20 PM

Disproving that a particular space is Banach

measure-theory lp-spaces
Updated October 20, 2018 15:20 PM

The set of points reached exactly $n$ times is measurable

analysis measure-theory measurable-functions
Updated October 20, 2018 13:20 PM

Reweighting Radon Nikodym Derivative

probability-theory measure-theory radon-nikodym
Updated October 20, 2018 13:20 PM

$\sigma$-algebra generated by set

measure-theory
Updated October 20, 2018 10:20 AM

Let A be the set of numbers in the interval [0, 1] that have the digit “0” in the first, second or third place in their decimal expansion

real-analysis measure-theory lebesgue-measure
Updated October 20, 2018 10:20 AM

Caratheodory measure $\bar{\mu}$ induced by $\mu$ and countable additivity

measure-theory
Updated October 20, 2018 05:20 AM

$(0,\infty)$ has Measure Zero with Given Measure

real-analysis measure-theory lebesgue-integral
Updated October 19, 2018 21:20 PM

Inseparable complete metric space with full Radon probability measure

general-topology measure-theory metric-spaces complete-spaces separable-spaces
Updated October 19, 2018 19:20 PM

showing that two distribution functions are the same

probability-theory measure-theory
Updated October 19, 2018 18:20 PM

Understanding Jordan decomposition of a function of bounded variation

real-analysis measure-theory
Updated October 19, 2018 18:20 PM

Integral of a function with respect to the measure $\nu(A)=\int_{A}fd\mu$

integration measure-theory
Updated October 19, 2018 18:20 PM

Measurability of the sum of measurable functions $(X_t)_{t \in I}$ ranging over a random index set $N$.

probability-theory measure-theory stochastic-processes stochastic-calculus stochastic-analysis
Updated October 19, 2018 15:20 PM

Isoperimetric Inequality via Brunn-Minkowski is valid for every norm?

real-analysis inequality geometric-measure-theory
Updated October 19, 2018 14:20 PM

Semi ring and sigma ring on Real line interval excercise

real-analysis measure-theory proof-verification
Updated October 19, 2018 11:20 AM

A confusion over the lebesgue outer measure of $(0,1) \cap \mathbb{Q}^c$

measure-theory lebesgue-measure
Updated October 19, 2018 11:20 AM

What is the sample space for the experiment : each hour approximately 12 people come in the shop.

probability measure-theory
Updated October 19, 2018 10:20 AM

Equality in Brunn-Minkowski inequatily. Problem 8 in Real Analysis Stein Chapter 1, Page 48.

real-analysis measure-theory lebesgue-measure geometric-measure-theory
Updated October 19, 2018 06:20 AM

$φ(t) = \int f(t, ω)dμ(ω)$ defines a real-valued continuous function on $(a,b)$

measure-theory
Updated October 19, 2018 06:20 AM

Understanding why almost everywhere pointwise convergeence implies convergence in measure.

real-analysis measure-theory
Updated October 19, 2018 01:20 AM

If for each $\epsilon > 0$, there is an open set $O$ containing $E$ for which $m^*(O-E) < \epsilon$, then $E$ is measurable set.

real-analysis measure-theory lebesgue-measure
Updated October 19, 2018 00:20 AM

Does Grothendick's theorem hold for Bounded borel functions?

functional-analysis measure-theory banach-spaces
Updated October 19, 2018 00:20 AM

Problems proving that if $f_n\rightarrow f$ pointwise and $\int_R f=\lim_{n}\int_R f_n$ then $\int_E f=\lim_{n}\int_E f_n$ for meas $E \subseteq R$.

real-analysis measure-theory lebesgue-integral
Updated October 18, 2018 23:20 PM

Verification of result

probability probability-theory measure-theory stochastic-processes stochastic-calculus
Updated October 18, 2018 21:20 PM

What does mod 0 mean in the context of ergodic theory?

measure-theory dynamical-systems ergodic-theory
Updated October 18, 2018 20:20 PM

Let $\Omega $ countable. Why the Borel $\sigma$-algebra is the power set?

probability measure-theory
Updated October 18, 2018 19:20 PM

Occupation measure of Brownian motion and absolute continuity

probability-theory measure-theory brownian-motion
Updated October 18, 2018 17:20 PM

Show that $\mathfrak B(\mathbb R)$ contains all countable subsets of $\mathbb R$

measure-theory borel-sets borel-measures
Updated October 18, 2018 17:20 PM

Royden "Real Analysis", 3rd edition, chapter 4, exercise 9

real-analysis analysis measure-theory lebesgue-integral
Updated October 18, 2018 17:20 PM

Problem in determining a map, given in the polar coordinate, is Area preserving or not on $\Bbb{R^2}$

calculus real-analysis measure-theory
Updated October 18, 2018 15:20 PM

Determining whether an interval (0,1] $\in\mathfrak B(\mathbb R)$ or not.

measure-theory borel-sets borel-measures
Updated October 18, 2018 13:20 PM

What is the term of the structure: "set of countable disjoint unions generated by a semi-ring"?

measure-theory terminology definition lebesgue-measure
Updated October 18, 2018 11:20 AM

Define a measure on the power set

measure-theory
Updated October 18, 2018 10:20 AM

$m^(A \cup B) = m^(A) + m^*(B) $ implies $A$ and $B$ are measurable?

measure-theory
Updated October 18, 2018 10:20 AM

Show that A belongs to the σ-algebra generated by the intervals and Find m(A), where m denotes Lebesgue measure

measure-theory
Updated October 18, 2018 09:20 AM

If $X$ is a Borel set and $f$ has countably many discontinuities, prove that $f:X\rightarrow \mathbf{R}$ is Borel measurable.

real-analysis measure-theory borel-sets
Updated October 18, 2018 08:20 AM

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