Question

Let (X,M, μ) be a measure space. Let (fn)n∈N be a sequence of

nonnegative measurable functions on X such that fn → f as n → [infinity] on
X and suppose that R X f = limn→[infinity] R X fn < [infinity]. Then fo

Answer 1

The college-level mathematics question focuses on a scenario in measure theory, involving the convergence of nonnegative measurable functions and their integrals over a measure space.

Step-by-step explanation:

The question pertains to a concept in mathematics, specifically within the realm of measure theory, which is a part of real analysis. The scenario describes a sequence of nonnegative measurable functions (fn) that converge to a function f over a measure space (X, M, μ), with the additional information that the integral of f over X is finite. The question might imply the application of the Lebesgue Dominated Convergence Theorem or another convergence theorem, which are crucial results in measure theory that allow one to interchange limit operations and integration under certain conditions.