# probability theory – Equivalence of two finite measures

My question is somehow similar to these equations in here, in here, and in here

let $$mu_1$$ and $$mu_2$$ be the two measures on $$mathbb R$$ such that
$$mu_1((a,b))= mu_2((a,b)) < infty$$ whenever $$−infty < a < b < infty$$ for which $$mu_{1}({ a})=0$$, $$mu_{1}({ b})=0$$,
$$mu_{2}({ a})=0$$, and $$mu_{2}({ b})=0$$. Show that $$mu_1(A) = mu_2(A)$$ whenever $$A in mathcal B$$.​

I am not sure how would I use $$pi$$-system and $$lambda$$-systme in here. Any hints are appreciated.