Re: A set containing a nonempty open interval

A N Niel <anniel@xxxxxxxxxxxxxxxxxxxxx> writes in article <260820051428574700%anniel@xxxxxxxxxxxxxxxxxxxxx> dated Fri, 26 Aug 2005 14:28:57 -0400:
>In article <denmfc$o5k$1@xxxxxxxxxxxxxxxxxxx>, Keith A. Lewis
><klewis@xxxxxxxxxxxxxxxx> wrote:
>
>> "Amanda" <sca18@xxxxxxxxxxx> writes in article
>> <1125067955.450481.88600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> dated 26 Aug 2005
>> 07:52:35 -0700:
>> >
>> >I'd like some hints on how to prove that, if a set S has positive
>> >Lebesgue measure, then (A + A)/2 = {(x + y)/2 | x and y are in A}
>> >contains a non-empty open interval.
>>
>> Unless you specify x <> y, you might get all closed intervals.
>
>By "contains a non-empty open interval" he means it has a subset which
>is a non-empty open interval.

Since every interval has a subset which is an open interval, I wonder why
the word "open" is even in the question. Probably not important, I guess.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

Relevant Pages

  • Re: continuous functions
    ... continuity. ... The above may not represent the opinions of my employer. ... Prev by Date: ...
    (sci.math)
  • Re: minimisation of a function
    ... Do you know anything about the coefficients a, b, c, such as their sign? ... The above may not represent the opinions of my employer. ... Prev by Date: ...
    (sci.math)
  • Re: Least primes in arithmetic progressions
    ... Dirichlet's theorem states that the series a*n+b contains an infinite number ... The above may not represent the opinions of my employer. ... Prev by Date: ...
    (sci.math)
  • Re: help with diophantine equation
    ... Options after that include factoring, modulo arithmetic, and the quadratic ... The above may not represent the opinions of my employer. ... Prev by Date: ...
    (sci.math)
  • Re: E of E = t*k*p
    ... The result is called a "gradient". ... The above may not represent the opinions of my employer. ... Prev by Date: ...
    (sci.math)