Struct ProductMeasure 

pub struct ProductMeasure {
    pub domain1: MeasurableSet,
    pub domain2: MeasurableSet,
}

Product measure μ₁ ⊗ μ₂ on a product space X₁ × X₂.

By Fubini’s theorem, for non-negative measurable f: ∫_{X₁×X₂} f d(μ₁⊗μ₂) = ∫_{X₁} (∫_{X₂} f(x,y) dμ₂(y)) dμ₁(x)

For Lebesgue measures this reduces to iterated integration.

Fields

domain1: MeasurableSet

First factor domain.

domain2: MeasurableSet

Second factor domain.

Implementations

impl ProductMeasure

pub fn new(domain1: MeasurableSet, domain2: MeasurableSet) -> Self

Create a product measure from two domains.

pub fn measure_product_box(&self, a: &MeasurableSet, b: &MeasurableSet) -> f64

Measure a product box A × B under the product Lebesgue measure.

(λ₁ ⊗ λ₂)(A × B) = λ₁(A) · λ₂(B)

pub fn product_domain(&self) -> MeasurableSet

Compute the product domain as a single concatenated box.

pub fn fubini_integrate( &self, f: &dyn Fn(f64, f64) -> f64, n_x: usize, n_y: usize, ) -> f64

Integrate a function f(x, y) over the product domain using Fubini.

Uses a simple grid rule: n_x × n_y quadrature points.

pub fn verify_fubini(&self, f: &dyn Fn(f64, f64) -> f64, n: usize) -> (f64, f64)

Verify Fubini’s theorem numerically: iterated vs. direct Monte Carlo.

Trait Implementations

impl Clone for ProductMeasure

fn clone(&self) -> ProductMeasure

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ProductMeasure

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.