The Linearity of Integration Part 1
The linearity property of integration will be something you are all well familar with from calculus.
You are well justified in using it in calculus as both the Riemann and Lebesgue integrals obey this property.
In this video we will prove that the property holds true for the Riemann integral (the formal form of integration we have thus far been studying).
The proof takes a little longer than you might expect. In a past video in this real analysis playlist we proved linearity for differentiation and that proof was extremely quick. The reason for that is we had already done most of the heavy lifting in previous videos when we had proved the algebra of limits for limits of functions.
The proof of linearity for integration uses some properties of suprema and infima which we have not previously used in this playlist and we will need to justify these as we go through.
