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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2000 • Question 1

Question

Math 6210 • Real Analysis 2000 • Question 1

Let \(f\) and \(g\) be two real valued measurable functions on a measurable space \(X\). Show that \[ \{x\in X:\sin f(x)\ge \cos g(x)\} \] is a measurable subset of \(X\).

Raw LaTeX

Let \(f\) and \(g\) be two real valued measurable functions on a
measurable space \(X\). Show that
\[
\{x\in X:\sin f(x)\ge \cos g(x)\}
\]
is a measurable subset of \(X\).

Topic Tags

Measurable Functions