Extensions
The dominated convergence theorem applies also to measurable functions with values in a Banach space, with the dominating function still being non-negative and integrable as above.
Read more about this topic: Dominated Convergence Theorem
Famous quotes containing the word extensions:
“The psychological umbilical cord is more difficult to cut than the real one. We experience our children as extensions of ourselves, and we feel as though their behavior is an expression of something within us...instead of an expression of something in them. We see in our children our own reflection, and when we don’t like what we see, we feel angry at the reflection.”
—Elaine Heffner (20th century)
“If we focus exclusively on teaching our children to read, write, spell, and count in their first years of life, we turn our homes into extensions of school and turn bringing up a child into an exercise in curriculum development. We should be parents first and teachers of academic skills second.”
—Neil Kurshan (20th century)