if ƒ1, ƒ2, ƒ3, … is a sequence of uniformly bounded real-valued measurable function which converges pointwise on a bounded measure space (S, Σ, μ) (i.e. one in which μ(S) is finite) to a function ƒ, then the limit ƒ is an integrable function and
Wednesday, November 23, 2011
Bounded Convergence Theorem
This is the mathematical definition of the Bounded Convergence Theorem (BCT):
if ƒ1, ƒ2, ƒ3, … is a sequence of uniformly bounded real-valued measurable function which converges pointwise on a bounded measure space (S, Σ, μ) (i.e. one in which μ(S) is finite) to a function ƒ, then the limit ƒ is an integrable function and
if ƒ1, ƒ2, ƒ3, … is a sequence of uniformly bounded real-valued measurable function which converges pointwise on a bounded measure space (S, Σ, μ) (i.e. one in which μ(S) is finite) to a function ƒ, then the limit ƒ is an integrable function and
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment