L p -SPACES IN MATHEMATICAL ANALYSIS

Abstract

In functional analysis, a great deal of time is spent with normed linear space, banach space, inner product space, many other spaces like Hilbert space, Lp -space etc.L p -space is a great field in functional analysis. L p -space play a central role in many questions in analysis. Here, we’ll focus on the fundamental structural information about the L p -space. This more abstract viewpoint also has the unanticipated benefit of guiding us to the unexpected finding of a finitely additive measure on all subsets that is consistent with Lebesgue measure. Here we will be familiar with measurability,measure space, measurable functions and Borel set etc. Lebesgue integral, integration of complex numbers, Lebesgue domi nated convergence theorem, dual of L p -space, two norm convergence in L p -space etc. also define here.