Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Un exemple de fonction int\'egrable sur [-1, 1] mais pas sur [0, 1]   In courses on integration theory, Chasles property is usually considered as
elementary and so "natural" that this is sometimes left to the reader. When the
functions take their values in finite dimensional spaces, the property is
always verified, but it no more true in infinite dimensional spaces. We first
give an easy-to-understand example of a function f from [-1, 1] into the space
of polynomial functions from [0, 1] to R which is integrable on [-1, 1] but not
on [0, 1]. We also provide a way of representing graphically such a function
which explains what means the integral of a function with values in an infinite
dimensional space. Then we show that Chasles'property is true if and only if
the space in which the functions to integrate take their values is a complete
space.

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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat