Lecture 2: Outer measures, construction of the Lebesgue measure.

[@小小学生-r5o]

I am still confused about what happened in 28:40. Why can we just simply add something to the left and then change the inequality the other way around?

[@thierryrioual701]

Because that's the definition of the infimum: For all a in A, and for all epsilon > 0, a - epsilon < inf A =0, and epsilon >0, epsilon/2^k > 0. See "Infima and suprema of real numbers": en.wikipedia.org/wiki/Infimum_and_supremum Normally the inequality is strict but by taking epsilon arbitrarily close to zero the inequality becomes loose.

[@asbjrnandersen4765]

lambda star is the infimum of the RHS. thats why adding a number greater than zero flips the inequality

[@HuggableJohn]

If you add a positive number to the greatest lower bound of a set, that number is no longer a lower bound of the set.

[@TheMorhaGroup]

"I hope you're as excited as I am😐😑😐"

[@darrenpeck156]

Could this criteria lead from countable subadditivity to countable additivity?

[@thomasjefferson6225]

disjoint unions for countable additivity

[@nicholaskhawli4330]

Isnt finite union concluded from the 2 sets union proof ? I guess u could prove it but shouldnt it be trivial

[@nicholaskhawli4330]

Why use inequality and add the epsilon if we will just equal it to zero . Then why not just use equality .