MARC Record from marc_columbia

LEADER: 04286mam a22003494a 4500
001 3050758
005 20221019205213.0
008 010418t20012001nyu b 001 0 eng
010 $a 2001028937
020 $a0824705351 (alk. paper)
035 $a(OCoLC)ocm46882619
035 $9ATL8338CU
035 $a3050758
040 $aDLC$cDLC$dC#P$dOrLoB-B
042 $apcc
050 00 $aQA312$b.L395 2001
082 00 $a515/.43$221
100 1 $aLeader, Solomon,$d1925-$0http://id.loc.gov/authorities/names/n2001008220
245 14 $aThe Kurzweil-Henstock integral and its differentials :$ba unified theory of integration on R and R[superscript n] /$cSolomon Leader.
260 $aNew York :$bMarcel Dekker,$c[2001], ©2001.
300 $aviii, 355 pages ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aPure and applied mathematics ;$v242
504 $aIncludes bibliographical references (p. 347-349) and index.
505 00 $tThe Gauge-Directed Integral.$tDifferentials.$tGuidance for the Reader --$gCh. 1.$tIntegration of Summants.$tCells, Figures and Partitions.$tTagged Cells, Divisions, and Gauges.$tThe Upper and Lower Integrals of a Summant over a Figure.$tSummants with Special Properties.$tUpper and Lower Integrals as Functions on the Boolean Algebra of Figures.$tUniform Integrability and Its Consequences.$tTerm-by-Term Integration of Series.$tApplication of Term-by-Term Upper Integration.$tIntegration over Arbitrary Intervals --$gCh. 2.$tDifferentials and Their Integrals.$tDifferential Equivalence and Differentials.$tThe Riesz Space D=D(K) of All Differentials on K.$tDifferential Norm and Summable Differentials.$tConditionally and Absolutely Integrable Differentials.$tThe Differential dg of a Function g.$tThe Total Variation of a Function on a Cell K.$tFunctions as Differential Coefficients.$tThe Lebesgue Space L[subscript 1] and Convergence Theorems --$gCh. 3.$tDifferentials with Special Properties.
505 80 $tProducts Involving Tag-Finite Summants and Differentials.$tContinuous Differentials.$tArchimedean Properties for Differentials.$tDifferentials on Open-Ended Intervals.$t[sigma]-Nullity of the Union of All [sigma]-Null Cells.$tMappings of Differentials Induced by Lipschitz Functions.$tn-Differentials on a Cell K --$gCh. 4.$tMeasurable Sets and Functions.$tMeasurable Sets.$tThe Hahn Decomposition for Differentials.$tMeasurable Functions.$tStep Functions and Regulated Functions.$tThe Radon-Nikodym Theorem for Differentials.$tMinimal Measurable Dominators --$gCh. 5.$tThe Vitali Covering Theorem Applied to Differentials.$tThe Vitali Covering Theorem with some Applications to Upper Integrals.$t[nu](1[subscript E]df) and Lebesgue Outer Measure of f(E).$tContinuity [sigma]-Everywhere of [rho] Given [rho][sigma]=O --$gCh. 6.$tDerivatives and Differentials.$tDifferential Coefficients from the Gradient.$tIntegration by Parts and Taylor's Formula.$tA Generalized Fundamental Theorem of Calculus.
505 80 $tL'Hopital's Rule and the Limit Comparison Test Using Essential Limits.$tDifferentiation Under the Integral Sign --$gCh. 7.$tEssential Properties of Functions.$tEssentially Bounded Functions.$tEssentially Regulated Functions.$tEssential Variation --$gCh. 8.$tAbsolute Continuity.$tVarious Concepts of Absolute Continuity for Differentials.$tAbsolute Continuity for Restricted Classes of Differentials.$tAbsolutely Continuous Functions.$tThe Vitali Convergence Theorem --$gCh. 9.$tConversion of Lebesgue-Stieltjes Integrals into Lebesgue Integrals.$tBanach's Indicatrix Theorem.$tA Generalization of the Indicatrix Theorem with Applications --$gCh. 10.$tSome Results on Higher Dimensions.$tIntegral and Differential on n-Cells.$tDirect Products of Summants.$tA Fubini Theorem.$tIntegration on Paths in [Riemann integral][superscript n].$tGreen's Theorem --$gCh. 11.$tMathematical Background.$tFilterbases, Lower and Upper Limits.$tMetric Spaces.$tNorms and Inner Products.$tTopological Spaces.$tRegular Closed Sets.
505 80 $tRiesz Spaces.$tThe Inclusion-Exclusion Formula.
650 0 $aHenstock-Kurzweil integral.$0http://id.loc.gov/authorities/subjects/sh86004388
830 0 $aMonographs and textbooks in pure and applied mathematics ;$v242.
852 00 $bmat$hQA312$i.L395 2001