Determine whether a set is subspace or not

  • Thread starter mithila
  • Start date
  • #1
mithila
1
0
The set of all functions f such that the integral of f(x) with respect to x over the interval [a,b] is
1. equal to zero
2. not equal to zero
3. equal to one
4. greater than equal to one
etc.

How can we determine this types of set is a subspace of not.



for the case of the set of continuous function we can easily check the closure conditions but for integrable function how can we check that.

can anyone help me to solve this type of problem

Thanks.
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,309
49
Usually, you just check the conditions. For example, take two functions f and g whose integral over [a, b] is zero, and check that the integral of (f + g) over [a, b] is also zero, etc.
 

Suggested for: Determine whether a set is subspace or not

Replies
4
Views
480
Replies
17
Views
801
Replies
3
Views
926
Replies
10
Views
220
Replies
3
Views
307
  • Last Post
Replies
17
Views
385
  • Last Post
Replies
4
Views
248
Replies
32
Views
517
Top