 Lp space

The space $L^p$ consists of measurable functions with finite $p$-norm, identified when they agree almost everywhere. This quotient is necessary because the integral seminorm vanishes on functions supported on null sets.

In functional analysis, an \( L^p \) space (or Lebesgue \( p \)-space) is a vector space of measurable functions for which the \( p \)-th power of the absolute value is integrable.

Integrable functions to the power $p$, usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of $L^p$ is complete but Riemann isn't