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.
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The space consists of measurable functions with finite -norm, identified when they agree almost everywhere. This quotient is necessary because the integral seminorm vanishes on functions supported on null sets.
Integrable functions to the power , usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of is complete but Riemann isn't