I am trying to calculate a lebesgue integral, or even finding if one exists. I am given the following function: $g(x)=\text{the greatest integer less than or equal to $x$}$
I must first show that it induces a measure, and I think it does since g is monotone increasing and right continuous. Is this true?
If it does induce a measure $\gamma$ (which I am pretty sure it does from my reasoning above), how can I calculate $\int_{[-11/2,13/2]}x^2d\gamma(x)$ ?
I am pretty sure the answer to this integral is just a number.
I am not familiar with how to explicitly calculate lebesgue integrals.