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Convergence in Lp spaces means that a sequence of functions {$f_n$} converges to a function f in the Lp norm if $\lim_{n\to\infty} \|f_n - f\|_p = 0$.

Hölder's inequality is a fundamental inequality in Lp spaces stating that for functions f in Lp and g in Lq, where 1/p + 1/q = 1, the integral of the product fg is less than or equal to $\|f\|_p\|g\|_q$.

The dual space of an Lp space, for 1 < p < infinity, is Lq where 1/p + 1/q = 1. The dual space consists of all bounded linear functionals on Lp.

A measurable function is one for which the preimage of any Lebesgue measurable set is also Lebesgue measurable. These functions are the building blocks of Lp spaces.

An Lp space is complete, meaning that every Cauchy sequence of functions in this space has a limit within the space. This makes Lp spaces Banach spaces for 1 <= p <= infinity.

Minkowski's inequality provides a triangle inequality for Lp spaces, stating that for all f and g in an Lp space, $\|f + g\|_p \leq \|f\|_p + \|g\|_p$ when 1 <= p <= infinity.

The L1 space, also known as Lebesgue space, consists of integrable functions, where the integral of the absolute value of the function is finite.

The L2 space contains all square-integrable functions, i.e., functions whose squares' integral is finite. This space is important in quantum mechanics and Hilbert space theory.

The Riesz-Fischer Theorem ensures the completeness of Lp spaces by showing that any Cauchy sequence in Lp, given certain conditions, converges in the Lp norm to a function within Lp.

A dense subset in an Lp space is a subset such that for every function in the Lp space, there is a sequence of functions within the subset that converges to it in the Lp norm.

Fatou's Lemma states that the integral of the limit inferior of a sequence of non-negative measurable functions is less than or equal to the limit inferior of the integrals of these functions.

An Lp space is a function space defined by the set of measurable functions for which the p-th power of the absolute value is Lebesgue integrable, where 1 <= p < infinity.

The L-infinity space is the space of essentially bounded functions, where a function f is essentially bounded if there exists a real number M such that the absolute value of f is less than or equal to M almost everywhere.

The norm of a function f in an Lp space, denoted by $\|f\|_p$, is defined as $(\int |f|^p dx)^{1/p}$ for 1 <= p < infinity.