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Both spaces are defined using the same set-builder principle: they are the collections of all measurable functions for which the corresponding norm (either the p-norm or the infinity norm) is finite.

Conditions: The context is the summary of $L^p$ and $L^\infty$ definitions.; Both $\|f\|_p$ and $\|f\|_\infty$ have been defined.

Both spaces are defined using the same set-builder principle: they are the collections of all measurable functions for which the corresponding norm (either the p-norm or the infinity norm) is finite.

Conditions: The context is the summary of $L^p$ and $L^\infty$ definitions.; Both $\|f\|_p$ and $\|f\|_\infty$ have been defined.

The L^$\infty$ space is defined as the set of all measurable functions whose infinity norm is strictly less than positive infinity.

Conditions: f is a measurable function.; The infinity norm $\|f\|_\infty$ has been defined.

The L^$\infty$ space is defined as the set of all measurable functions whose infinity norm is strictly less than positive infinity.

Conditions: f is a measurable function.; The infinity norm $\|f\|_\infty$ has been defined.