Let ((Omega,Sigma,mu)) be a complete probability measure space and ((E,B(E))) be a measurable space, where E is a separable Banach space, (B(E)) is a Borel sigma algebra of E, ((Omega,Sigma )) is a measurable space (Σ-sigma algebra) and μ is a probability measure on Σ, that is, a measure with total measure one.
Let ((Omega,Sigma,mu)) be a complete probability measure space and ((E,B(E))) be a measurable space, where E is a separable Banach space, (B(E)) is Borel sigma algebra of E, ((Omega,Sigma)) is a measurable space (Σ-sigma algebra) and μ is a probability measure on Σ, that is, a measure with total measure one.
Let ((Z,mathcal{B}(Z))) be a measurable space and (pi(dv)) a σ-finite measure on it.
Let ((mathcal{X,U})) be a measurable space and let μ and ν be two probability measures defined on it.
Let ((X,mu)) be a measurable space.
Let ((Omega, S)) be a measurable space.
Let ((Omega,mathcal{F})) be a measurable space.
Example 2.3 Let ( S, S ) be a measurable space.
We denote by a complete probability measure space (briefly, a measure space), where is a measurable space, is a sigma algebra of subsets of, and is a probability measure.
In particular, when H = L 2 ( A, A, μ ), where ( A, A ) is a measurable space and μ is a σ-finite and non-atomic measure, one has that H ⊗ q = L S 2 ( A q, A ⊗ q, μ ⊗ q ) is the space of symmetric and square integrable functions on A q.
A tone is not a point on a musical plane; it is a measurable space with top and bottom limits.
