If $\mu$ and $\nu$ are measures on $X$ and $Y$, is there an example of a set $E\subset X\times Y$ such that $E_x,E^y$ are measurable for all $(x,y)$ but $E$ is not measurable with respect to $\mu\times\nu$?
2026-03-27 01:46:38.1774575998
Example of Non-Measurable Sets in Product Space
420 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MEASURE-THEORY
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Absolutely continuous functions are dense in $L^1$
- I can't undestand why $ \{x \in X : f(x) > g(x) \} = \bigcup_{r \in \mathbb{Q}}{\{x\in X : f(x) > r\}\cap\{x\in X:g(x) < r\}} $
- Trace $\sigma$-algebra of a product $\sigma$-algebra is product $\sigma$-algebra of the trace $\sigma$-algebras
- Meaning of a double integral
- Random variables coincide
- Convergence in measure preserves measurability
- Convergence in distribution of a discretized random variable and generated sigma-algebras
- A sequence of absolutely continuous functions whose derivatives converge to $0$ a.e
- $f\in L_{p_1}\cap L_{p_2}$ implies $f\in L_{p}$ for all $p\in (p_1,p_2)$
Related Questions in EXAMPLES-COUNTEREXAMPLES
- A congruence with the Euler's totient function and sum of divisors function
- Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$
- Inner Product Uniqueness
- Metric on a linear space is induced by norm if and only if the metric is homogeneous and translation invariant
- Why do I need boundedness for a a closed subset of $\mathbb{R}$ to have a maximum?
- A congruence with the Euler's totient function and number of divisors function
- Analysis Counterexamples
- A congruence involving Mersenne numbers
- If $\|\ f \|\ = \max_{|x|=1} |f(x)|$ then is $\|\ f \|\ \|\ f^{-1}\|\ = 1$ for all $f\in \mathcal{L}(\mathbb{R}^m,\mathbb{R}^n)$?
- Unbounded Feasible Region
Related Questions in PRODUCT-SPACE
- Open Set in Product Space Takes a Certain Form
- Set of Positive Sequences that Sum to 1 is Compact under Product Topology?
- $ \prod_{j \in J} X_{j} $ is locally connected if, and only if, each $ X_{j} $ is locally connected ...
- Dense subspaces of $L^\infty(\Omega\times\Omega)$
- $\{0,1\}^{\mathbb{N}}$ homeomorphic to $\mathbb{R}$?
- Understanding product topology
- The topology generated by the metric is the product topology of discrete space {0,1}
- Show that $(X,d)$ is compact
- For a discrete topological space $X$, is Perm$(X)$ a topological group as a subspace of product topological space $X^X$?
- Uniform distribution Measure
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?