Category:Product Measure
Jump to navigation
Jump to search
This category contains results about Product Measure.
Let $\struct {X, \Sigma_X, \mu}$ and $\struct {Y, \Sigma_Y, \nu}$ be $\sigma$-finite measure spaces.
Let $\struct {X \times Y, \Sigma_X \otimes \Sigma_Y}$ be the product measurable space of $\struct {X, \Sigma_X}$ and $\struct {Y, \Sigma_Y}$.
The product measure of $\mu$ and $\nu$, denoted $\mu \times \nu$, is the unique measure with:
- $\forall E_1 \in \Sigma_X, E_2 \in \Sigma_Y: \map {\paren {\mu \times \nu} } {E_1 \times E_2} = \map \mu {E_1} \map \nu {E_2}$
Subcategories
This category has the following 2 subcategories, out of 2 total.
F
- Fubini's Theorem (2 P)
T
- Tonelli's Theorem (4 P)
Pages in category "Product Measure"
The following 4 pages are in this category, out of 4 total.