The proof of theorem is wrong

Let’s create a very simple measurable spaceMathworldPlanetmathPlanetmath: X={a,b}, 𝒜={,{a},{b},X}.

Let’s take the π-system P={{a}} containing only one subset of X.

Let’s create two measuresMathworldPlanetmath μ=δa+δb and ν=δa+2δb. Then obviously μ and ν agree on P and are finite, but they obviously are not equal on 𝒜.

The proof, however, claims that it is sufficient if μ and ν are finite. I believe that μ(X)=ν(X) is a necessary condition.

Title The proof of theorem is wrong
Canonical name TheProofOfTheoremIsWrong
Date of creation 2013-03-22 19:16:05
Last modified on 2013-03-22 19:16:05
Owner tomprimozic (26284)
Last modified by tomprimozic (26284)
Numerical id 4
Author tomprimozic (26284)
Entry type Example
Classification msc 28A12