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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.

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

Conditions: The p-norm $\|f\|_p$ has been defined.; f is a measurable function.

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

Conditions: The p-norm $\|f\|_p$ has been defined.; f is a measurable function.