Groups
Category
Level
A Banach space is a vector space with a norm where every Cauchy sequence actually converges within the space.
A Hilbert space is an inner product space that is complete, meaning Cauchy sequences converge to points inside the space.
Lebesgue integration measures how much time a function spends near each value and adds up value × size of the set where it occurs.
A σ-algebra is a collection of subsets that is closed under complements and countable unions, giving us a stable universe of sets where measure makes sense.