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This is from Analysis by Lieb :

''Things the reader is expected to know : While we more or less start from 'scratch' , we do expect the reader to know some elementary facts, all of which will have been learned in a good calculus course . These include : vector spaces , limits , lim inf, lim sup , open , closed and compact sets in ]Rn, continuity and differentiability of functions ( especially in the multivariable case ) , convergence and uniform convergence ( indeed , the notion of 'uniform ', generally ) , the definition and basic prop erties of the Riemann integral , integration by parts ( of which Gauss' s theorem is a special case ) . ''

Is this covered in all rigourous calculus books?

Is this book any harder than the by Carothers or Berberian?

''Things the reader is expected to know : While we more or less start from 'scratch' , we do expect the reader to know some elementary facts, all of which will have been learned in a good calculus course . These include : vector spaces , limits , lim inf, lim sup , open , closed and compact sets in ]Rn, continuity and differentiability of functions ( especially in the multivariable case ) , convergence and uniform convergence ( indeed , the notion of 'uniform ', generally ) , the definition and basic prop erties of the Riemann integral , integration by parts ( of which Gauss' s theorem is a special case ) . ''

Is this covered in all rigourous calculus books?

Is this book any harder than the by Carothers or Berberian?

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