Interchanging a limit and an integral: necessary and sufficient conditions
Abstract Let { f n } n ∈ N $\{f_{n}\}_{n \in \mathbb {N}}$ be a sequence of integrable functions on a σ-finite measure space ( Ω , F , μ ) $(\Omega, \mathscr {F}, \mu )$ . Suppose that the pointwise limit lim n ↑ ∞ f n $\lim_{n \uparrow \infty } f_{n}$ exists μ-a.e. and is integrable. In this settin...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-11-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02502-w |