Beppo Levi's theorem establishes the value of this operation on the pointwise limit of a pointwise monotonic sequence of functions. This operation's value for the limit inferior of a sequence of functions is less than or equal to the lim-inf of its values for those functions according to Fatou's lemma. This operation's name
Beppo Levi's theorem establishes the value of this operation on the pointwise limit of a pointwise monotonic sequence of functions. This operation's value for the limit inferior of a sequence of functions is less than or equal to the lim-inf of its values for those functions according to Fatou's lemma. This operation's namesake showed how the existence of a larger function establishes its value for a smaller function in his (*) dominated convergence theorem. The space of functions to which this operation may be applied is a Banach space, in which continuous compactly-supported functions form a dense subset. This operation, which may be applied to functions in the Lp spaces, gives equal values for functions that differ only on a set of measure zero. It recapitulates the results of another method that approximates the area under a curve using rectangles. For 10 points, name this operation that extends the Riemann integral to measure spaces.
Beppo Levi's theorem establishes the value of this operation on the pointwise limit of a pointwise monotonic sequence of functions.
Lebesgue integral [or Lebesgue integration; prompt on integral or integration; do not accept "Riemann integral" or "Riemann integration"]