Real analysisVan Nostrand, 1959 - 272 pages |
Contents
CHAPTER 0PRELIMINARIES SECTION PAGE 1 Sets 1 1347 | 1 |
SECTION | 2 |
Functions and Relations | 3 |
Copyright | |
45 other sections not shown
Common terms and phrases
absolutely continuous Baire function basic neighborhood bounded variation characteristic function closed interval cluster point compact contained continuous functions converges defined definition denote derivative directed function disjoint domain equation exercise exists f is continuous field F follows Fourier function f Hausdorff space Hence induction inequality integer integral intervals of continuity Io(e L-functions Lebesgue LEMMA Let f lim f(x lim inf f(x lim sup lim sup f(x limit linear space lower semicontinuous m-measurable m-summable maximality principle me/ne measurable functions measurable sets metric space n-tuple N₁ natural numbers non-negative nonempty notation open interval open set ordered field ordered pairs partially ordered set polynomial positive integer positive number PROOF prove rational subfield real number real-valued functions Riemann-Stieltjes integrable sequence step-function subdirected function summable suppose supremum THEOREM topological space U-function upper bound Y₂ zero