Why the custom deleter doesn't increase the size of unique_ptr object?

Question

I have written this test code:

int main(int argc, const char * argv[]) {
    int *testRaw = nullptr;
    cout << sizeof(testRaw) << endl;

    unique_ptr<int> testUnique(nullptr);
    cout << sizeof(testUnique) << endl;

    auto CustomeDeleter = [](int *ptr)
    {
        cout << *ptr;
        delete ptr;
    };

    unique_ptr<int, decltype(CustomeDeleter)> testUniqueCustom(nullptr, CustomeDeleter);
    cout << sizeof(testUniqueCustom) << endl;

    return 0;
}

With the compiler clang-700.1.81 my output is:

8
8
8

How could it be that the custom deleter didn't increase the pointer size? As I understand lambda function is an object of the closure type, and the size of any class always > 0 in C++. Thank you for your help!